(since operations on infinity are either infinity or undefined, except division by infinity which typically yields 0)
#help-0
night geyser
like its totally possible to do this but its just not a useful thing to do and it adds a lot of complications to our system
and now all our theorems need to be phrased with "let x be a complex number that's not infinity..."
youll see it if you end up doing high-level mathematics (complex analysis, differential geometry, etc) but its not really worth it at a lower level
now thats just the riemann sphere - its natural to ask if theres another way to divide by 0 thats more algebraically well-behaved
there have been multiple attempts at this
one people often reference is wheel theory, which seeks to be an algebraic structure where dividing anything by anything is always allowed
theres a problem: wheel theory is utterly useless
like it is genuinely just a curiosity, no one has found any serious reason to study it
so its been relegated to a "fun fact: we can technically do this" type deal
rather than something taken seriously
but it does exist, so that you can say "technically, there is a context where division by 0 is perfectly fine"
this context is just way, way more complicated than standard arithmetic.
tl;dr its possible to do, sometimes (riemann sphere) its even useful, usually it isnt — but at a non-advanced level, its typically more effort and confusion than its worth
in general, the answer to "Why can't we do [x]" in mathematics is rarely "it's utterly impossible"; instead, its usually "doing so is way more trouble than it's worth and has some negative consequences on the wider structure"
width?
surreal crystal
Nah my bad
Misunderstood what you were talking about
I can add that it can make sense to divide zero
1/0 is a distinct object
Namely we only really know that 0*(1/0)=1
But hey, that means something
Just not a number
lone heartBOT
@main ruin Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
naive aspen
Can someone help me with this problem?
lone heartBOT
Can someone help me with this problem?
alpine sable
Can someone help me with this problem?
try drawing a secant line
like unsing a secant line
zenith olive
hi
zenith olive
celest blaze
Use trigonometric functions
tan(x) = o/a
We can take o = altitude, and a is the distance
zenith olive
tan(x) = o/a
yeah but idrk how to do it
how do i find the distance
actually what distance am i meang to find
zenith olive
how do i find a or x
celest blaze
x is angle, o is altitude
celest blaze
Try drawing a triangle to represent the situation
zenith olive
is x 5 or 1.5
celest blaze
The short leg will be height, the long leg will be distance
the angle between the hypoteneuse and the long leg is the angle of depression
celest blaze
Plug both numbers into the equation, then find the difference
That gives you distance travelled
zenith olive
tan(1.5)=400/a
tan(5)=400/a ??
celest blaze
yes, solve for a
celest blaze
Yes, those are the correct distances
celest blaze
yes, that is the distance travelled
celest blaze
yes
zenith olive
now i just solve for speed
celest blaze
Yes, you want to convert that to km/h
zenith olive
oh
right
uhhh
ii think i did smth wrong
10703.3628 divided by 2
thats in 1 min
5351.6814
oh wait no
right
and times that by 60
321100.884
m
divide by 1000
= 321km/h
OHH
OKK
tysmmm
celest blaze
np :)
celest blaze
Sure!
celest blaze
for the first one, start by ignoring the 60 degree angle
use the 3 and the 20 degrees to find the length of the long leg
celest blaze
oh kk
Use algebra to write an expression for the long leg
l = 10+n
then use that as the length to find x
tan(25) = x/(10+n)
tan(50) = x/n
U should be able to solve for x
celest blaze
If you isolate n in both of the equations, then equate them, you should get x
celest blaze
Bc the lone variable will dissappear
zenith olive
uhh for the 2nd one i can solve for n but could u help withe the first please
celest blaze
x/tan(25)-10 = n
zenith olive
oh yeah i just got that and was gonna ask u if it was right lol
the other is x/tan(50)=n?
celest blaze
x*tan(50)/tan(25)-10*tan(50)=x
-10*tan(50)=x-x*tan(50)/tan(25)
-10*tan(50)=x(1-*tan(50)/tan(25))
Something like than, then isolate x
zenith olive
uhh is there like an easier way to solve this perhaps 💀
celest blaze
idk, any way I can think of is similar
sin(50) = x/n, sin(25) = x/(n+10)
n = x/sin(50), sin(25) = x/(n+10)
sin(25) = x/((x/sin(50))+10)
zenith olive
💀💀
😭
this is too complicated for my pea brain
like i couldd use the cosine rule, but im not allowed to use it for this question so 💀
lone heartBOT
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zenith olive
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alpine sable
Class: Intro to Linear Algebra; Topic: Differential Equations;
alpine sable
I would like to verify that this answer is correct. Some other classmates have had issues with this question and I would like verification before taking it to the professor.
Here is my work.
limpid turret
By inspection I immediately see that y1' is wrong
limpid turret
Here is my work.
Most people won't open attachments here. Post screenshots.
limpid turret
Step 4
Your last -0+1 needs to be -0-1
The fact that you still got integer solutions in your cubic was admittedly kinda unlucky
@alpine sable
alpine sable
your talking about when taking the determinant?
@limpid turret
I did make that mistake originally. The eigenvalues should be correct though.
that notation was from a prior attempt which was missed in correction.
limpid turret
Nah the eigenvalues you wrote are for the cubic with the wrong coefficients
alpine sable
So matrix A is incorrect?
limpid turret
Hold on
It's actually correct
But only because you wrote -28 instead of +28 in your last submatrix
You just got really lucky that the two mistakes worked out there
alpine sable
The determinant again. My apologies with that.
I corrected it in the step above, but did account for every instance that I missed a sign.
Did mess up with the eigenvectors then?
Or the diagonal?
limpid turret
Your second eigenvector doesn't look right. But I can't really read it
alpine sable
Is P called the eigen matrix? P2 can be seen there.
P2 was [-1/7, 1, t] but was multiplied by 7 to keep it in whole numbers.
and the t removed.
limpid turret
P2 was [-1/7, 1, t] but was multiplied by 7 to keep it in whole numbers.
This is incorrect form. All components should have t
But I can see that what you eventually get for P2 is correct
P3 is also correct
You didn't finish your work
$Y=Pe^DP^{-1}$
ocean sealBOT
SWR
limpid turret
That's why it's not correct
You need to find P^-1
I'm off to bed now
Good luck
lone heartBOT
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Available help channel!
harsh swallow
I need some help. I need to prove that $A \Leftrightarrow B$ but i only know how to prove $\neg A \Rightarrow \neg B$
ocean sealBOT
Katharine
worn fox
Are we meant to be guessing what you're trying to prove?
echo socket
You prove that by showing A -> B and B -> A are both true
harsh swallow
sorry i meant to add can i use this
i need to prove f is injective if and only if f has a left inverse
but i only know how to prove that if f is not injective f does not have a left inverse
worn fox
That only proves half of the statement
echo socket
By contrapositive that's the same as f has left inverse -> f is injective
So now you need to show f is injective -> f has left inverse
harsh swallow
i do not know how to because i feel like i'm pulling stuff from my ass when i try
worn fox
You have to explicitly construct a left inverse
harsh swallow
the problem is i don't see why it is forbidden for a map to have the property of a1 != a2 meaning f(a1) != f(a2) and not a left inverse
all i have is these definitions
worn fox
Maybe try and see what goes wrong if you tried to find a left inverse of the function f(x) = x² in the reals
harsh swallow
that i understand but that is proving the not A therefore not B
not injective therefore no left inverse
but that doesn't mean injective therefore left inverse
lone heartBOT
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@harsh swallow Has your question been resolved?
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potent forge
Simplify/find the derivative of ln(5x)/x^2. The answer I got was x-2xln(5x)/x^4, but the task says the answer is actually -2ln(5x)/x^3, why did the two x'es above disappear and not the one in ln(5x)?
worn fox
Your second term is exactly exactly what they have, simplify using power laws
Why you also have a +x is impossible to say without seeing your work
potent forge
I used the quotient rule to get the answer I got, since ln(5x)=1/x and 1/x * x^2 becomes x, take that minus ln(5x)*2x which just is 2xln(5x) and all of this divided by x^4
Its a fraction, so I had to use the quotient rule to get that answer
It just seemed like I fell one step short
Which I know
potent forge
But why didnt ln(5x) lose its x?
harsh swallow
$\frac{d}{dx} \frac{\ln(5x)}{x^2}$
ocean sealBOT
Katharine
harsh swallow
right?
vale wigeon
since ln(5x)=1/x
misuse of equals sign.
harsh swallow
no the original
potent forge
Your second term is exactly exactly what they have, simplify using power laws
Why didnt those laws affect the 5x inside ln?
worn fox
Why would it?
potent forge
Because 2x isn't raised to any power, just like 5x or the standalone x?
worn fox
Also the answer is not just -2ln(5x)/x³
potent forge
Thats what it said in the guide
harsh swallow
what expression do you have to take the derivative of?
worn fox
Your second term has x/x⁴ in it which is 1/x³
vale wigeon
but the task says the answer is actually -2ln(5x)/x^3
can you please show us where it says that
worn fox
Oh you're not using bracket correctly
vale wigeon
yes even if its in arabic we still want to see it
worn fox
You mean you got (x-2xln(5x))/x⁴ 
keen bear
Factor an x out
potent forge
Sorry
Yes, at the cost of x^4, makes sense, thats why its becomes the power of 3, im just confused why it doesnt affect ln at all since it has an x inside of it as well
keen bear
ln(5x) is not a multiplication, it is a function with an argument.
worn fox
The 5x can't "see" the division by x⁴
It's inside a function that doesn't care what's happening outside
keen bear
It's like how sin(2x)/x doesn't simplify to sin(2)
potent forge
but the final answer, itl be (1-2ln(5x))/x^3 then?
Since zac brought up a good point of x/x is 1 and not just, gone
worn fox
but the final answer, itl be (1-2ln(5x))/x^3 then?
Yep
wraith flame
lone heartBOT
wraith flame
Hallo guys can you help me answer no. 9
alpine sable
Since we know one officer will be woman already, that leaves us with only 4 possibilities left, two men and two women
wraith flame
yes then the probability is 50 50 rigth?
prime badge
it's 1/3 tho
lone heartBOT
@wraith flame Has your question been resolved?
prime badge
it's 1/3
like it's not really a contradiction to say 1/2, since they don't say what "randomly" means
if it's equally likely to be 1-1, 2-0, 0-2, that's still random
but this sort of question is never like that
wraith flame
if it's equally likely to be 1-1, 2-0, 0-2, that's still random
what is the meaning of this?
lone heartBOT
wraith flame
.reopen
lone heartBOT
✅
prime badge
man+woman, woman+woman, man+man
if they choose in a way that gives these results equal probability, you can say the answer is 1/2
and that's still "random"
wraith flame
but they already chose one and that a woman and there is just one spot left
prime badge
they don't choose like that, they just choose 2 people
it's not like they chose one woman
they already chose both people
maybe they chose 2 women, maybe not, but it's not half and half
there's 9 possibilities where one person is a woman
call them AB | CDE
AC ,AD, AE, BC, BD,BE, CD,CE,DE
3 out of 9 is 2 women
that's how you're meant to interpret it
solemn juniper
Two child paradox wearing a fake moustache
prime badge
girl-boy
wraith flame
wait but here its asking what is the probability of 2 woman is chosen
prime badge
yes
conditioned, "updated" on the information that one is a woman, there's no argument about that
wraith flame
call them AB | CDE
AC ,AD, AE, BC, BD,BE, CD,CE,DE
mmmh im still confused
prime badge
you can't just imagine they chose 1 woman, they already chose both people
you're told they are not both men
you just examine all possibilities
one thing to notice is you already almost knew what they told you, it was 90% that at least one is a woman anyway
wraith flame
call them AB | CDE
AC ,AD, AE, BC, BD,BE, CD,CE,DE
ohh so thats what it means
now im starting to get it
ok now I get it thank you for all the help
.close
tepid aurora
lone heartBOT
limpid spade
,rotate
ocean sealBOT
surreal crystal
We can reciprocate the x and set the limit to 0 here
Then we can use lhopitals rule easily
random steppe
🤓
limpid spade
or u can stimulate it into the form of euler limit
tepid aurora
Using hospital i must
surreal crystal
Its certainly easier with lh
Just set x=1/y, then y->0 and its in the form to do lh
placid swallow
or with Taylor series
tepid aurora
Wait what
lone heartBOT
@tepid aurora Has your question been resolved?
olive kestrel
need help to derive this
lone heartBOT
need help to derive this
carmine reef
product rule
lone heartBOT
@olive kestrel Has your question been resolved?
ocean hawk
you can treat -288(x - 9) as one function
olive kestrel
because -288 derives to 0 ?
ocean hawk
well because it's a valid function
you can write it as -288x + 2592 (or whatever it multiplies out to) if you like
olive kestrel
ah I get what u mena
mean
solutions also suggest to multiply -0,1 into (x-9)²
but its a part of the mutliplication can I just do that ?
lone heartBOT
Available help channel!
soft stag
hello
gray jewel
Hello there
gray jewel
I'm not sure what the question wants
soft stag
its a two way table
tiny dew
I think I could help @soft stag
soft stag
alright
tiny dew
At least as far as I understand
soft stag
alright
tiny dew
okay, so, do you know how to calculate the probability here?
tiny dew
I mean, what do you think is the probability of a mid school student (being chosen at random) being in favor?
soft stag
Because a Decimal is /100
soft stag
I mean, what do you think is the probability of a mid school student (being chos...
1.5
wwait no
tiny dew
And how did you come to this conclusion?
tiny dew
yes
you do the same with not in favor
and, as you will be able to see, .25 and 150/200 = .75 add up to 1
soft stag
yea
soft stag
yup
i think i can do the rest
60300
.2
and 240/300 = .8
means its 20% for favor and 80% for non
(Highschool)
tiny dew
exactly
tiny dew
whoa
soft stag
lmao
tiny dew
nope~
soft stag
ong/
tiny dew
you've got that total column
soft stag
alright
tiny dew
you can't add percentages like this
soft stag
ahhh
tiny dew
very illegal here
tiny dew
neither
soft stag
oh
tiny dew
look at this bit
it's all you need here
treat it like you did with mid schoolers and high schoolers b4
soft stag
copy them down?
tiny dew
not really
soft stag
but it maked sence
bc thats what they did for the same thing
50+60=110
OH
its bc they arnt doing it in percentages
tiny dew
when you wanted to calc. the probability of "in favor", you divided the number of (mid/high) schoolers in favor by the number of every student
it's basically the same here
tiny dew
where did you even get that 45 from
tiny dew
oh dear
the total of in favor is 50 (mid) + 60 (high)
which equals 110
the total of not in favor is 150 (mid) + 240 (high)
which equals 390
the total number of all students is equal to 500
so when you have all of those 500 students in a room, and you want to see which ones are in favor, you need to divide the number students in favor by the number of all students
tiny dew
good job cowboy
tiny dew
coming back to that previous ex. for one last time
soft stag
tiny dew
there's a formula for that
tiny dew
gimme a second
soft stag
alroight
tiny dew
the first one is good
soft stag
alr
tiny dew
and the second one's good too
tiny dew
soft stag
right?
tiny dew
I mean, yea, sure, it is correct
tiny dew
but I don't recommend playing like that on a big test
tiny dew
yes, we have room full of students and pointing randomly, we want to choose a student who's in 8th grade and prefers studying at the library
tiny dew
there's a formula for that
probability = A set or a number of favorable events divided by all events
at least here
lone heartBOT
lone heartBOT
Available help channel!
minor goblet
hey can someone explain how the 0.46773 becomes 1.46773?
lone heartBOT
hey can someone explain how the 0.46773 becomes 1.46773?
mortal trellis
-x-0.46773x = (-1-0.46773)*x = -1.46773x
minor goblet
where does the -1 come from?
mortal trellis
-x = -1*x
minor goblet
ooooh
mortal trellis
yes
minor goblet
wtf
lime holly
Yes
mortal trellis
you have -1 apple and then -0.46773 apples and together that gives -1.46773 apples
minor goblet
oh.
ok that makes total sense now
hm so if i had 1 apple and -0.46773 apple came it wuld be 0.53227 apples?
barren aurora
Hey, I am doing an assignment where I have to explain the proofs of the different Pythagorean theorems. Our teacher required us to do Euclid's bride chair (or windmill) proof and allowed us to choose our second. He told us not to choose one that is not difficult, or that doesn't require much math. I was wondering if anyone here was familiar with a proof similar to the difficulty of the bride chair one and could potentially provide resources that help explain it? Thank you so much!
gray jewel
Hey, I am doing an assignment where I have to explain the proofs of the differen...
This maybe?
(a + b)^2 - 2ab = c^2
a^2 + b^2 = c^2
They are pretty similar
lone heartBOT
@barren aurora Has your question been resolved?
barren aurora
That helps but I've seen this one before, is there maybe more a little bit more challenging?
@gray jewel
gray jewel
That helps but I've seen this one before, is there maybe more a little bit more ...
I mean you can google it
gray jewel
That helps but I've seen this one before, is there maybe more a little bit more ...
Here's a proof of it using a trapezoid
From google images
But I don't think you should be asking that
polar fulcrum
Guys how can I solve these , they’re for an assignment I have
But I can’t really understand it
lone heartBOT
@barren aurora Has your question been resolved?
deep girder
Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 327 with 44% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.
lone heartBOT
@deep girder Has your question been resolved?
lone heartBOT
@deep girder Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
scarlet quarry
Here's my question here, and my work so far. I have absolutely no clue why it doesn't work for 2 and 4.
lone heartBOT
Here's my question here, and my work so far. I have absolutely no clue why it do...
@scarlet quarry Has your question been resolved?
scarlet quarry
<@&286206848099549185>
lone heartBOT
@scarlet quarry Has your question been resolved?
scarlet quarry
Well I presume nobody here knows at this point
scarlet quarry
Figured it out, I used 16 for both vectors, not 13 for the second
That took too long for me to figure out
.close
candid ginkgo
Can someone help me with how I figure this out, I'm not sure what I should do with the extra number in the intersection
candid ginkgo
.close
night spade
the formula for volume of a pyramid is lwh/3 right? what did i do wrong
bitter kestrel
lwh/3 is for a square pyramid, you have a triangular pyramid so you have to divide that in half to get lwh/6
coarse oasis
why is the integral of 3cos(pi/2x) = 6/piSin(pi/2)??
lone heartBOT
why is the integral of 3cos(pi/2x) = 6/piSin(pi/2)??
lone heartBOT
Please read #❓how-to-get-help
random junco
oops my bad
lone heartBOT
@coarse oasis Has your question been resolved?
coarse oasis
<@&286206848099549185>
proven leaf
why multiply by the reciprocal of the inside
$\int_{0}^{2}{3\cos\left(\frac{\pi}{2}x\right)}dx=3\int_{0}^{2}{\cos\left(\frac{\pi}{2}x\right)}dx$ and $\int\cos(\frac{\pi}{2}x)dx=\frac{2}{\pi}\sin\left(\frac{\pi}{2}x\right)$ so to answer your question, we just multiplying reciprocal
ocean sealBOT
XxMrFancyu2xX
lone heartBOT
proven leaf
👍
peak mist
help
surreal crystal
because an/an+1 is what we use to check convergence
we take |an/an+1|=L here
if L < 1, it converges
if L > 1, it diverges
if L = 1, the test fails
we want the biggest and smallest x that make L < 1
their difference is the radius of convergence
does this make sense?
peak mist
thank you
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Available help channel!
rotund crater
someone can demonstrate me tan^-1(tan x) = x
lone heartBOT
someone can demonstrate me tan^-1(tan x) = x
north hemlock
someone can demonstrate me tan^-1(tan x) = x
$f^{-1}(f(x)) = x$
ocean sealBOT
Juke | ping me if no response
north hemlock
the inverse of the function and the fucntion essentially "cancel out"
alpine sable
i mean like same idea when u use ln for exponantioal functions
isnt the ln the invers of e
north hemlock
ah
okay
I read what u wrote as "it's taking the ln of both sides or or rasing to the power e"
north hemlock
$f^{-1}(f(x)) = x$
$f(f^{-1}(x))= x$
ocean sealBOT
Juke | ping me if no response
rotund crater
the inverse of a function "undoes" what the function does
i dont understand
you mean is 1?
north hemlock
you mean is 1?
wym
where is 1 coming from
there are no numbers here
the idea is that a function can have an inverse function, and they undo one another
$\tan^{-1}$ is the inverse of $\tan$
ocean sealBOT
Juke | ping me if no response
rotund crater
the idea is that a function can have an inverse function, and they undo one anot...
I don't think they are canceled like this because yes, why are they canceled, does it become one? or something else happens
north hemlock
okay so I think I found the issue
ur trying to visualize it I assume?
hope this helps
bitter sage
can anyone help with this
lone heartBOT
can anyone help with this
bitter sage
i understand i have to use u subsitution but how what do i do with the sqrt(4 - x^2)
naive valley
i understand i have to use u subsitution but how what do i do with the sqrt(4 - ...
could just integrate that separately?
lone heartBOT
@bitter sage Has your question been resolved?
silver wasp
lone heartBOT
silver wasp
Can someone explain the second step to the third. I dont understand it
carmine reef
$\int f(x)+g(x)~dx = \int f(x)~dx + \int g(x)~dx$
ocean sealBOT
RedstonePlayz09
carmine reef
$\int cf(x)~dx = c\int f(x)~dx$
ocean sealBOT
RedstonePlayz09
carmine reef
you mean how do you go from the first step to the second?
silver wasp
Ye
carmine reef
you have to set $\frac{Ax+B}{x^2+1} + \frac{C}{x+1} = \frac{3x^2-4x+5}{(x+1)(x^2+1)}$
ocean sealBOT
RedstonePlayz09
carmine reef
remember you're solving for A,B,C here, not x
carmine reef
that's not how you add fractions
carmine reef
that and the numerator isn't quite right
carmine reef
no
it seems like at some point you misapplied a distribution law or something
remember that $(a+b)*c = ab + ac$, not $a + bc$
ocean sealBOT
RedstonePlayz09
lone heartBOT
@silver wasp Has your question been resolved?
chrome garnet
dms open if anyone wants to explain in specifis
lone heartBOT
dms open if anyone wants to explain in specifis
surreal crystal
dms open if anyone wants to explain in specifis
You have this entire channel
chrome garnet
thanks
surreal crystal
What do you need help with
chrome garnet
basically everything except 1a
surreal crystal
Alr
You can do all of 1 on your calculator
To start i will write the definition of log
chrome garnet
1b divide .25 by 8?
surreal crystal
No
chrome garnet
oh its 8 by .25
surreal crystal
,w calculate log_8 .25
ocean sealBOT
chrome garnet
is that mutliplicagtion?
surreal crystal
No
chrome garnet
how does it get .6?
surreal crystal
$\log_{a}(a^b)=b=a^{\log_{a}(b)}$
ocean sealBOT
Cycadellic
surreal crystal
This is the definition of log
It essentially “undoes” our a^b
It tells us the b
Whereas root would tell us the a
Make sense?
Youre not gonna calculate this by hand
Very long and tedious
We need a calculator for it
surreal crystal
Lets say $a=\log_{2}(64)$
ocean sealBOT
Cycadellic
surreal crystal
Then $2^a=64$
ocean sealBOT
Cycadellic
chrome garnet
oh okay
surreal crystal
,w calculate log_2(64)
ocean sealBOT
chrome garnet
jes i had help with that one in class
surreal crystal
And to check
chrome garnet
im still confused as to how you know which number it equals to
surreal crystal
,w calculate 2^6
ocean sealBOT
chrome garnet
,w 8^.66666666666
ocean sealBOT
surreal crystal
Its guess and check basically
chrome garnet
look why does that one say 3.99
chrome garnet
wasnt that the answer though???
ocean sealBOT
surreal crystal
Make sense?
surreal crystal
-.6666666666≈2/3
surreal crystal
Computers can only calculate so much
chrome garnet
,w log(8) .25
ocean sealBOT
chrome garnet
what??????????/
surreal crystal
_
chrome garnet
its given 3 different answers so far
ocean sealBOT
chrome garnet
so .6 =2/3
brave island
.
surreal crystal
Yeah
chrome garnet
have you heard of mathway?
chrome garnet
i tried punching in log_3 -9 but it said cannot solve?
surreal crystal
Cause negatives are tricky
chrome garnet
can you explain negatives in logs
surreal crystal
We are restricted a lot by - times - = +
Some negatives you cant get
(Unless you just make up a number that makes i^2=-1, but thats beyond this)
chrome garnet
oh because its like -x-x-x-x-x- and so on?
chrome garnet
right
surreal crystal
oh because its like -x-x-x-x-x- and so on?
Did you mean times negative?
chrome garnet
negative times - times negative times -
surreal crystal
I see
surreal crystal
We can really multiply a number by itself to get - so all negative logs are undefined
Just do 1 on a calculator
Ill help you with 2 and the rest
$log_{x}(4x-3)=2$
ocean sealBOT
Cycadellic
ocean sealBOT
Cycadellic
surreal crystal
Definition of log
chrome garnet
right
surreal crystal
How do i get log_x off the left of =
surreal crystal
**Cycadellic**
On this one
chrome garnet
a^log_a?
surreal crystal
No
chrome garnet
since theres no number with the log
surreal crystal
You wont ever learn if youre never wrong
Focus on what is in the subscript
That little letter a little lower than the reat
chrome garnet
the big a?
surreal crystal
$log_{x}(4x-3)=2$
ocean sealBOT
Cycadellic
chrome garnet
the little x
ocean sealBOT
Cycadellic
chrome garnet
the second part is super confusing
surreal crystal
**Cycadellic**
This is the rule
chrome garnet
you dont mean subtract do you?
surreal crystal
This is what log means
surreal crystal
**Cycadellic**
This is the equation in 2a
surreal crystal
**Cycadellic**
Do you see how doing a^log_a gives us just whats on the inside of log?
surreal crystal
Because a is the base of the exponent, and a is the subscript on the log
surreal crystal
Because a is the base of the exponent, and a is the subscript on the log
The definition of log, the way we want it to work, is to do this
This is just what we mean by log
chrome garnet
like 2^6 being the 6 is the sub?
surreal crystal
I dont follow
chrome garnet
me neither dude
chrome garnet
my teacher isnt too good at explaining things
surreal crystal
$b=a^{\log_{a}(b)}$
chrome garnet
language barrier kinda
ocean sealBOT
Cycadellic
chrome garnet
not really
surreal crystal
This is telling us how to remove the log
If he have the log base and the exponent base the same, they cancel
Like addition and subtraction
chrome garnet
log base is little a?
surreal crystal
Yeah
chrome garnet
exponenent base is the big a?
surreal crystal
They are the same a
We just make the log one smaller so we dont confuse it with whats inside
chrome garnet
so exponent base=log base
surreal crystal
No, when exponent base= log base, they cancel
chrome garnet
so 4x-3 would be the (b)
surreal crystal
Its the same as without () it just makes it clearer whats inside the log
Cause log x - 3 would be confusing
chrome garnet
okay but i still dont understand what you meant by removing the logx from the left
chrome garnet
$log_{x}(4x-3)=2$
ocean sealBOT
El Fran
chrome garnet
not at all
chrome garnet
x is subscript
surreal crystal
Do x^ on both sides
ocean sealBOT
Cycadellic
surreal crystal
There is only one possible number here right?
chrome garnet
yes
surreal crystal
So that means we can do it to both sides of the eq and it stays true
$log_{x}(4x-3)=2$
ocean sealBOT
Cycadellic
chrome garnet
i have to find x right
chrome garnet
i dont understand the way you phrase this
surreal crystal
We have an equation
Lets just say two variables to vastly simply so you can understand me
$a=b$
ocean sealBOT
Cycadellic
ocean sealBOT
Cycadellic
surreal crystal
When a=b is correct
surreal crystal
**Cycadellic**
This is also correct
Because there is only one possible thing i could get
Im not gonna put x^y in my calculator and get more than 1 number, yk
chrome garnet
right
surreal crystal
**Cycadellic**
So we wanna do this
chrome garnet
🫤
surreal crystal
Do you know what i mean by ^
chrome garnet
exponent
surreal crystal
No, it is x times itself, a times
chrome garnet
yeah x times x
surreal crystal
?
chrome garnet
im genuinely so lost right now
chrome garnet
lets just say no
but i know its x times by however many times the ^ is right
like i said 2^2 is 4?
surreal crystal
Yeah
chrome garnet
or is that not what youre meaning at alllll
surreal crystal
^ is exponent
chrome garnet
right yes
chrome garnet
its x times x
surreal crystal
$a=b$
ocean sealBOT
Cycadellic
chrome garnet
can we use numbers instead
surreal crystal
$.2=.20$
ocean sealBOT
Cycadellic
chrome garnet
okay yes
ocean sealBOT
Cycadellic
surreal crystal
**Cycadellic**
We did x^ to this equation
chrome garnet
like x^ to log makes it x^log
ocean sealBOT
El Fran
chrome garnet
is the goal for log to be the exponent here?
chrome garnet
and what would it be the exponent to?
surreal crystal
x, because its in the base of the log
chrome garnet
so instead of log_x itd translate to x^log
chrome garnet
it just adds another x?
surreal crystal
Write that one
chrome garnet
oh because you also turn 2 to exponent
surreal crystal
Right
chrome garnet
okay i got that part down