Can someone help me and explain how to do a few?

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[rain merlin]

$\logadd$

[sullen elbow]

wolfqz

[rain merlin]

$\logsubtract$

[sullen elbow]

wolfqz

[rain merlin]

these are the formulas

@hallow copper

[heady cedar]

bro has the macro ready

[rain merlin]

also $\log_d a^b = b\log_d a$ is used

[sullen elbow]

wolfqz

[rain merlin]

🔥

[hallow copper]

Okay, so how do I use the formulas for this?

[heady cedar]

$\log_{a^x} b^y = \frac{y}{x} \log_a b$ better

[sullen elbow]

(xy)²=(yz)²=(xz)²=xyyzxz=-1

[hallow copper]

Could one of you help me with one of them and then I can try to do one myself?

[heady cedar]

for 10)

$\log_7 (a³b⁶) = \log_7 a³ + \log_7 b⁶ = 3\log_7 a + 6\log_7 b$

[sullen elbow]

(xy)²=(yz)²=(xz)²=xyyzxz=-1

[rain merlin]

explain the logic too smh

[heady cedar]

basically reducing
from
expo -> multiply
root -> divide
multiply -> plus
divide -> minus

[sullen elbow]

wolfqz

[hallow copper]

How do you know which formula to use?

[heady cedar]

practice

[rain merlin]

well not really

if u have something like $\log_3 uv$ say, then u know just by looking that its like $\logadd$ so u apply that

[sullen elbow]

wolfqz

[hallow copper]

Bro, I’m asking which formula to use for each problem because there are multiple formulas. Wdym practice??

[rain merlin]

cuz its in the form log_d ab^^

@hallow copper

[heady cedar]

well if you practice you will get used to the math and you will know which one to use

[hallow copper]

“Mommy, how you divide a fraction?” The mom doesn’t provide an answer and just says “practice” without explaining how to do it. Essentially, that’s what you just did to me.

[rain merlin]

Bro

why aint u reading what i sent

😭

[hallow copper]

I am

[rain merlin]

didnt that help

[hallow copper]

No, I just learned this concept today so I am very new and just a little confused on the topic.

[rain merlin]

do u know the properties of logarithms
Just think in what form the question is and apply that property

[rain merlin]

do u know the properties

[hallow copper]

No

[rain merlin]

Ah

let me explain it for u then

so logarithms are just reverse of exponentiation

u know what exponentiation is right? @hallow copper

[hallow copper]

No, never even heard that term before. Is my teacher smoking something?

[rain merlin]

$a^b$

[sullen elbow]

wolfqz

[rain merlin]

exponentiation

raising to the power of something

[hallow copper]

Ok

Makes sense

[rain merlin]

u know that?

right

[hallow copper]

Ya

[rain merlin]

Alright then

logarithms work like this

$\log_a b = m \implies a^m = b$

[sullen elbow]

wolfqz

[rain merlin]

So basically its used for finding exponents

if your given $a^m = b$ then $m = \log_a b$

[sullen elbow]

wolfqz

[rain merlin]

@hallow copper do u understand

[hallow copper]

Yes

[rain merlin]

alright now

time to prove the properties

so

[heady cedar]

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/a/properties-of-logarithms

[rain merlin]

Let $p = \log_a x$ and $q = \log_a y$

[sullen elbow]

wolfqz

[heady cedar]

try going through this

[rain merlin]

let me present the proof yo

[rain merlin]

@hallow copper we start with this, if $p = \log_a x$ then $a^p = x$ by definition of logarithm

[sullen elbow]

wolfqz

[rain merlin]

similarly $y=a^q$

[sullen elbow]

wolfqz

[rain merlin]

@hallow copper do u understand till here

[hallow copper]

You know what, I couldn’t be more lost honestly. This isn’t helping. Sorry. Thanks for trying to help but this is just no use.

[rain merlin]

wdym 😭

i started from the definition

and worked my way up

[rain merlin]

u can take the logarithms course on khan academy ^^

[hallow copper]

I’m just really mad rn as you can tell by my facial expression bro. And yes, that’s actually me.

It’s just not helping. Sorry

[rain merlin]

🔥

[hallow copper]

But thanks anyways

[rain merlin]

Try taking the course on khan academy maybe thatll help

im no professional teacher so they will teach better than me ofc

[tall crane]

yea seeing as text explaining isn’t really working I’d recommend watching videos on it @hallow copper