Logarithms Bsae

[true bridge]

<@&286206848099549185>

[dense isle]

Do you know the change of base formula for logarithms?

[true bridge]

yea

@dense isle

[dense isle]

So you can apply them here

It wants you to put them in base 3

[true bridge]

so

can we use the formula

log a b = log c b / log c a

[dense isle]

Yes

[true bridge]

ok

i got 1/ 2 log 2 ^3 - 1/ 2 log 8 3

• 1 / log 8 3

what would we do next

[dense isle]

Wait

If log (base a) of b is log (base c) of b/ log (base c) of a, what is the inverse?

in other words what is 1/(log (base a) of b)?

[true bridge]

yea i wrote it in the equation

[dense isle]

So I’d write your equation as log of something / log of something

[true bridge]

is this correct

[dense isle]

for example the first fraction, i’d write it as log 2 / log 9

Im not sure

[true bridge]

wait wdym

[dense isle]

I’d use the change of base formula

[true bridge]

ok the first one is 1/ 2 log 2^3

[dense isle]

But since it’s 1/ log, the fractions flip

[true bridge]

so how would we rewrite it

[dense isle]

Wait why log 2^3

Oh yea

But i’d rewrite as log2/log 9

[true bridge]

isnt the base supposed to be 3

@dense isle

[dense isle]

Yes

[true bridge]

Could u solve it and tell me what u get @dense isle

[dense isle]

Ok well ive simplified the first fraction as (log base 3 of 2)/2

Also I don’t think I can just solve it for you

[true bridge]

Could u help me work through for the second and third

@dense isle

[dense isle]

Yea

[true bridge]

ok

so how do we do the next one

[dense isle]

So write just log base 8 of 9 using the change of base formula

and let c be 3

[true bridge]

1/ 2 log8 3?

[dense isle]

No with the change of base formula

[dense isle]

this

[true bridge]

so

we got 8 9

log 3 8^/9?

@dense isle

[dense isle]

Well it’s log base 3 of 8 / log base 3 of 9

[true bridge]

yep

[dense isle]

and log base 3 of 9 is what

[true bridge]

2

[dense isle]

Yes

so the second fraction is (log base 3 of 8)/2

[true bridge]

ok last one

[dense isle]

So same thing

[true bridge]

1/ log 8 3

[dense isle]

Use change of base formula again

[true bridge]

log base of 3 8/ log base of 3 3

so its 1

[dense isle]

Well the denominator is 1

[true bridge]

yep

numerator is

log base 3 of 8

[dense isle]

Exactly

So what do you have in total

[true bridge]

log base 3 of 2 / 2 - log base 3 of 8 / 2 + log base 3 of 8

[dense isle]

So now we should make everything the same denominator

Making the last fraction the same would be easiest

[true bridge]

multiply by 2

[dense isle]

and divide by 2 so the fraction doesn’t change

so it’s 2 (log base 3 of 8)/2

and now you can combine the numerators of the fractions

[true bridge]

wait

so if we divide by 2

then whats it gonna be

or is it just for the las tone

[dense isle]

No just the last one

[true bridge]

kk

so we get

[dense isle]

To combine fractions the denominator needs to be the same

[true bridge]

log base 3 of 2 - log base 3 of 8

• 2 (log base 3 of 8)/2

[dense isle]

Yea and since they are all the same base we can do stuff with other log laws

Do you know the other log laws

[true bridge]

Yep

Log base 3 of 2 / log base 3 of 8

this would be 1/4?

[dense isle]

Not nessecarily

well what are the log laws

thé ones important rn are thé ones about adding and subtracting logs

[true bridge]

Yea

Adding and subtracting

if we add we multiply

and if we subtract we divide

@dense isle

[dense isle]

Yes

So what happens when we combine the 3 logs

[true bridge]

we use the laws

[dense isle]

mhm and it becomes one log

[true bridge]

yep

[dense isle]

base 3

ohh i see what you were saying

Yes it would be 1/4 but then you need to multiply the other log

[true bridge]

Yep

What would the other log be

2 x log base 3 of 8 /2

[dense isle]

yea

but that’s th same as log base 3 of 64 /2

So you multiply 1/4 with 64

[true bridge]

yep

and we get 16

[dense isle]

So what do you have in total

[true bridge]

uh

oh do we use logs for 64 x 1/4

[dense isle]

yes

[true bridge]

would it be 16

[dense isle]

yes

[true bridge]

it says its wrong tho

[dense isle]

wdym

what do you have

[true bridge]

i entered 16

[dense isle]

Oh no

It’s not 16

[true bridge]

Oh

[dense isle]

It’s log base 3 of 16 /2

Cuz the logs are still there and the /2 is still ther

[true bridge]

it says its wrong

yea this is wrong

[dense isle]

That is wrong?

[true bridge]

yea

thats what it says

@dense isle what is it

[dense isle]

No it’s right

Maybe we can simplify it

[true bridge]

yea

do we just multiply by 2

[dense isle]

uhh

This is wierd

[true bridge]

oh wait

we cant

nvm

[dense isle]

Ok so it’s definetly the same number

Maybe try 1/ log base 4 of 3

(I just used the change of base formula again on our previous answer in base 4)

[true bridge]

doesnt it have to be base 3

its wrong btw

[dense isle]

That’s what I thought

it said in its simplest form

[true bridge]

o yea

so what do i enter

[dense isle]

Oh wait u could do 2 log base 3 of 2

or log base 3 of 4

I used the log exponent rule

[true bridge]

I got it

[dense isle]

Did that work

[true bridge]

log base 3 of 4 was rightr

Yea

[dense isle]

oh ok yea

[true bridge]

do u have time

for another

or no

[dense isle]

what I did was i rewrote 16 as 4^2 and since it’s a log one log law says exponents go down and then it cancelled with the /2

Not exactly

[true bridge]

oh om

ok

[dense isle]

Sorry

[true bridge]

yea no problem

i appreciate u helping

thanks