maths

[prisma lava]

i need help 1.66 d.
thanks.

[hasty steeple]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
2. Wait patiently for a helper to come along.
3. Once someone helps you, say thank you and close the thread with:

   +close
   

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[dire surge]

What do you not understand? It's basically the same as the other three.

[stark forge]

Imagine it simply said 4^x = 4

In that case, x = 1

Now, what is 1^2? It is also 1. Indeed, 1 to the power of anything at all is 1.

So, considering what (d) is asking you, replacing x with 1 works fine.

[grim snow]

Well actually it's +1 and -1

Other than that what wardy said

[stark forge]

True, but I wouldn't rule out that at her level they would expect her to just write 1.

[dire surge]

...the precalculus level?

[stark forge]

I just hear it's common in school. But yes, writing that x = (plus-or-minus symbol)1 would be safer.

[dire surge]

This is logarithms they're learning, and they're working with e.

This is Calc 1 or precalc.

[grim snow]

Why do y'all use periods what's your problem 😭

[dire surge]

We like communicating clearly because we're competent mathematicians.

[grim snow]

Are u also expecting me to read your message in British accent

[stark forge]

The order at which content is presented, and level it is taught at, differs across countries.

[grim snow]

There is no log here lol

[stark forge]

I think he is referring to something she posted a few days ago. But even this is a way to learn logs.

[dire surge]

e is defined as the result of either a limit or a series. You cannot describe e without using some amount of calculus.

[grim snow]

How

[dire surge]

...if you know what a logarithm is that should already be obvious just from looking.

[grim snow]

To us it spawned out of nowhere

[stark forge]

Same here.

[grim snow]

But if I don't know then I won't know there is logs here

[stark forge]

I was told about log base e before ever learning e.

[grim snow]

[stark forge]

Still, no big deal.

[dire surge]

In which case you also won't know if there aren't.

[grim snow]

Lmao what

So I don't know it but I'm learning logs

I do all questions without knowing I actually learnt logs here

[dire surge]

You said there are no logarithms here. If you don't know what logarithms are, then you don't know enough to say whether they are or aren't present in this problem.

[grim snow]

I will not give in to your manipulation!

Anyway we going offtopic

[prisma lava]

i mean in the conclusion 1 and -1 is the right answer

[grim snow]

@prisma lava u know why there are two solutions right

[prisma lava]

yes we are learning about logarithms

[prisma lava]

yess i know

[grim snow]

Alright

[prisma lava]

wait let me reread everything ahaha

[grim snow]

Ur doing these with logs???

[dire surge]

...yes? That's the only way.

[grim snow]

[grim snow]

Comparison..???

[dire surge]

What does that even mean?

[grim snow]

Making the bases of LHS and rhs equal we can compare the exponents

[white shoal]

Taking logs implicitly instead of explicitly

[drowsy juniper]

Hey

[dire surge]

Prove it.

[drowsy juniper]

Ohh the issue of y √x²is mod x

[grim snow]

Okay take part a so I write 81 as 9^2 take that to LHS we get 9^(x-2)=1 so x-2=0 x=2

[dire surge]

...what???

[drowsy juniper]

My bad

[dire surge]

That's not a proof

[grim snow]

We can take variables instead of numbers

It will be proof

[white shoal]

It won't

You've used what you're proving

[dire surge]

Prove that a^x = a^y ==> x = y.

[grim snow]

Take a^y to LHS denominator

a^(x-y)=1

[grim snow]

That's only possible when exponent is 0

[prisma lava]

this is what we are having about

[grim snow]

X-y=0

X=y

[white shoal]

Yeah, just use logs lol

[prisma lava]

ahaha yes

[white shoal]

It's what youre learning about

[prisma lava]

the rule?

[white shoal]

What rule?

[drowsy juniper]

Mm here is a issue then prove 1/a^x as a^-x

[prisma lava]

in the book

wait

[drowsy juniper]

Cause proof is like step by step just saying

[prisma lava]

oh wait

[grim snow]

That's in laws of exponents base same powers subtract

[drowsy juniper]

I know but do you know how to prove it

[grim snow]

I mean yeah?

[prisma lava]

1/x is x^-1

[grim snow]

I know😄

@drowsy juniper

U want me to prove

[drowsy juniper]

Yep

[prisma lava]

but what are you guys even talking about 😭

[drowsy juniper]

Mm nothing just proof thing

[dire surge]

Can you prove that?

[prisma lava]

okok

[grim snow]

1/a^x = a^x whole to the power of -1 .. so x and -1 multiply to give -x

[white shoal]

No clue, they took over your channel for dome reason lol

But anyway, feel free to close the channel if you're done

[grim snow]

Are u taking me as deep into it to finally drag me to logs bro..

[dire surge]

I'm confused about what you found confusing about the problem.

[prisma lava]

ok so

[drowsy juniper]

Mm you never proved it

[prisma lava]

this is what i did for c

[grim snow]

it's like doing a trigonometry question and at every turn asking me to prove everything from scratch

[grim snow]

Proved what

[prisma lava]

and now i am confused on d because its 2 exponents

[grim snow]

@prisma lava

[prisma lava]

yess

[grim snow]

It's just x^2=1

Solve it u get x=+-1

[prisma lava]

and -1

[dire surge]

a^x * a^(-x) = a^(x - x) = a^0 = 1
a^(-x) = 1/a^x```

[prisma lava]

yes

[drowsy juniper]

Nvm this is not a proof but ok dont want to make it tough for sept to read the channel so i will leave it here

[grim snow]

Nooo

It's equal to 1

When u solve for x then x is equal to +-1

[prisma lava]

but -1*-1 is 1

[grim snow]

Yeah

[prisma lava]

yes

[drowsy juniper]

Makes sense

[prisma lava]

thats what i meant ahaha

[prisma lava]

but how did you get x^2 = 1

[drowsy juniper]

You learnt log?

[grim snow]

There are some predefined things used to prove other things u can't expect me to prove the theorums i use for proof even in exams they don't do that

[dire surge]

...log base 4 on both sides.

[prisma lava]

4 = 4^1

[grim snow]

Comparision

[drowsy juniper]

Exams is different

[dire surge]

For which you have no basis.

[grim snow]

4^x^2=4^1 so x^2=1 @prisma lava

[drowsy juniper]

But was curious my bad please continue

[prisma lava]

because u used log base 4?

[grim snow]

Prove to me how u can take log on both sides

[grim snow]

No but if u do I think ull get this only

[drowsy juniper]

He did a^x=a^y if x=y

[white shoal]

Logs are well-defined functions, qed

[grim snow]

I don't care prove me how u can take it

[dire surge]

Yes, even though they refuse to admit that's what they did.

[prisma lava]

ohh now i see

[grim snow]

@dire surge either way why take log base 4 just take log base e and cancel ln 4 both sides

[dire surge]

f is a function if and only if x = y ==> f(x) = f(y). The logarithm base 4 is a function. Therefore, x = y ==> log_4(x) = log_4(y).

[drowsy juniper]

I think we are confusing him due to squable better like one person give their solution then next so he sees both and picks what he wants

[dire surge]

...that is taking the log base 4.

[drowsy juniper]

And then debate

[dire surge]

There isn't more than one solution. There's one solution that one person here refuses to understand.

[drowsy juniper]

Mm i understand

Logarithm is the way but still

[dire surge]

That's literally just the change of base formula.

[grim snow]

It's not my fault that in my education system we did it without using logs.

[drowsy juniper]

Base changing theorum

[dire surge]

You didn't do it without using logs, you just did it without knowing you were using logs.

[drowsy juniper]

Yes till log was introduced yeah the only method was comparison

[grim snow]

It can be proved that my method is correct USING logs doesn't mean i used it.

[dire surge]

This is like saying you solved x + 3 = 5 without subtraction. No, you didn't.

[grim snow]

Also f(x) = a^x so f(x)=f(y) if and only if x=y @dire surge

Hence proved boom

[dire surge]

No, not if and only if.

[grim snow]

It's the same u used to prove your thing

Don't even argue this

[dire surge]

No it's not.

[grim snow]

Keep yappin

[drowsy juniper]

Mm ots monotonically increasing graph with no point of extremum

[dire surge]

x = y ==> f(x) = f(y) is a different statement from f(x) = f(y) ==> x = y.

[grim snow]

Screw u

Stop being a math teacher bruhh

[drowsy juniper]

This is true in case of point extremums

[dire surge]

...for... knowing logic?

[dire surge]

I don't care if it's true, I care that Corazon failed to prove it.

[grim snow]

@drowsy juniper yeah fight for me brother

I'm at wits and desire's end

Arguing with this guy

[drowsy juniper]

Mmm this is kindof targetting

[grim snow]

[dire surge]

...yes, I'm targeting a person who made a claim with a request to prove the claim.

[drowsy juniper]

Ok lets call it a truce of comprimise

Its his way you cant change it sadly atmost you can correct it

By pointing it out

[grim snow]

Yes

Theres nothing sad bout it

[dire surge]

If they just say shit without proving it they're a bad helper.

[drowsy juniper]

Then it depends on the other to accept or not his life his wish

[dire surge]

And they're harming the understanding of the people they're trying to help.

[drowsy juniper]

I guess the person understood it from the convo the poster

[drowsy juniper]

Half knowledge is bad true

[grim snow]

No one needs your PhD ass level understanding to do 10th grade questions

[dire surge]

Without a proof it's not knowledge at all.

[grim snow]

It's not that my answer lacked logic ur over exaggerating

[drowsy juniper]

But what guarantee you have he will not do it again after correcting so much sad reallity

[grim snow]

I didn't use any super shortcut that actually needed proof

[drowsy juniper]

Actually you do

[drowsy juniper]

It lacked essense so lets not start it

[drowsy juniper]

Actually you did so umm

[dire surge]

Yes you did. You did not ever once prove that a^x = a^y ==> x = y.

[grim snow]

I can't prove it without logs agreed

But does that mean i used logs

Even if it did

So what

I answered right

Then what's your issue

[dire surge]

Then you are wrong to claim that you didn't.

[drowsy juniper]

Bro one thing no one aint gonna change in this room so let it be

[prisma lava]

i just did this

the red one

[grim snow]

I'm not the one asking the question so whether or not I did it doesn't affect the one asking so doesn't matter

[dire surge]

Right, so what was confusing about that?

[drowsy juniper]

Nice

[dire surge]

You are the one saying the thing that is not true.

[drowsy juniper]

Mm halfass true

But ok

Calm

[grim snow]

But why does it matter

[dire surge]

No, the claim that he didn't use logarithms is just untrue.

[grim snow]

Even if it isn't true

[drowsy juniper]

That part is true

[white shoal]

Decent, though I wouldn't write sqrt(x^2)=sqrt(1), cause that itself doesn't say the solutions are +-1

[dire surge]

No, it's not.

[drowsy juniper]

What i supported your claim

[white shoal]

It says x has modulus 1, to which x=+-1

But regardless it's the correct steps

[dire surge]

Technically speaking, sqrt(1) = 1. You need to say sqrt(x^2) = +/- sqrt(1)

[grim snow]

Can u prove this

[white shoal]

Be literate, QED

[drowsy juniper]

Simple

[prisma lava]

i was just confused about how we got rid of 4 on both sides 😭

[drowsy juniper]

X²

Enjoy

[dire surge]

...can I prove that A ==> B is a different statement from B ==> A?

[drowsy juniper]

F(x)=x²

[prisma lava]

so we used log base 4

or not

because it makes sense

[dire surge]

Yes.

[prisma lava]

if we used that

okok

[white shoal]

Take log_4 of both sides
Log_4(4^(x^2))=log_4(4)
x^2=1

[drowsy juniper]

It was inherently present

[dire surge]

The same way as we got rid of the base for every other problem.

[drowsy juniper]

You just did not show it

[grim snow]

No that the latter part which YOU used is true

[prisma lava]

yess

[prisma lava]

makes sense

[drowsy juniper]

Hey try f(x) =x²

[prisma lava]

thank youu

[white shoal]

Anyway, any more questions or can we stop the embarrassment this channel has become?

[drowsy juniper]

Nope feel free to stop it

[white shoal]

I'm asking OP

[prisma lava]

i will close it now

[white shoal]

Sounds good

[prisma lava]

i am just gonna write some notes

[prisma lava]

this

[grim snow]

For my or his statement

[drowsy juniper]

Your

[grim snow]

Which statement

[drowsy juniper]

This statement is true

For f(x)=x²

[grim snow]

x=y thing?

[white shoal]

Well defined does not mean injective

[drowsy juniper]

Yeah try

[grim snow]

Yes if x=y then x^2 =u ^2

[prisma lava]

thank you

+close