Question

Log5(7)=a
Log5(6)=b
Log5(4)=c

Find log5(4/9)

Answer 1

what's the change of base formula ??

Answer 2

Isn't that when you have a calculator? I can't use calcu
Actor but the values give ..

Answer 3

I have to write it using the letters

Answer 4

to find log you have to use change of bae formula \[\huge\rm log_a b = \frac{ \log b }{ \log a }\]

Answer 5

do you have to change that log form to exponential form ?

Answer 6

No. I have to rewrite it with the letters.

Answer 7

ohh with log too ?

Answer 8

then yes just apply change of base formula
but don't plug in calculator

Answer 9

I'm sorry. Not find the log, but rewrite sorry!

Answer 10

I don't think that's the correct way.. The answer in my key is 2c-2b

Answer 11

wait a sec i thought those are 4 different questions ?

Answer 12

Oh no. The 4 on top is f the variables I use to rewrite the last log with

Answer 13

I mean 3 on the top

Answer 14

i'm sorry i don't understand what they are asking

Answer 15

@jim_thompson5910

Answer 16

Use the properties of logarithms and the logarithms provided to rewrite each logarithm in terms of the variables given

Answer 17

Based on your log laws

" Find log5(4/9) "
Just means log5 (4) - log5 (9).
So we know log5 (4) = c and log5 (9) = ....

Answer 18

I knew that for c.. But can't find log5(9)

Answer 19

It is like that for all my problems that I'm doing. I can find one but then I can find the other

Answer 20

@jim_thompson5910

Answer 21

OKAY! I have figured something out.. kinda LOL

we have log5(4/9) .
We want to manipulate the information that we are given to somehow end up with
log5(4/9)
So Let's firstly think of other fractions that are equivalent to 4/9.
---> The hints are in your given information like log5(6) and log5(4).
If we square 4, we get 16 right?
Square 6 and we get 36.
Now, does 16/36 = 4/9 ?
I think yeeeess ^_^
Therefore, we're going to want to use.
log5(4/9)

=log5(4)^2 - log5(6)^2

(then bring the 2 down to the front of the log)

= 2log5(4) - 2log5(6)
= 2c - 2b