# Math Help - Logs

1. ## Logs

i have two questions.

so one problem is:
2log(3x)-log(x)=2

i don't remember if you apply the 2 to the (3x) or if it's like algebra and you just divide it by 2 to cancel out. oh and then you'd divide log 3x by log x right to combine them because they have the same base?

the other one is:
15log base 1/3(1/27) + logbase 1/4(256)= u

so does the 15 go to the 1/3 or 1/27 or do you just divide it.
and you can't combine them because they have different bases right?

sorry if this is confusing..

2. Originally Posted by lonejunior
i have two questions.

so one problem is:
2log(3x)-log(x)=2

i don't remember if you apply the 2 to the (3x) or if it's like algebra and you just divide it by 2 to cancel out. oh and then you'd divide log 3x by log x right to combine them because they have the same base?

the other one is:
15log base 1/3(1/27) + logbase 1/4(256)= u

so does the 15 go to the 1/3 or 1/27 or do you just divide it.
and you can't combine them because they have different bases right?

sorry if this is confusing..
1)

2 log(3x) - log x = 2
2 (log 3 + log x ) - log x = 2

can you do it from here?

2)
example
$
log_{10}1000 = 3
$

thats because 10^3 = 1000
can you work out your second equation now?

3. thanks for the help.
i understand what you meant for the first problem and i was able to solve it
and i understand the example you gave me, but i don't understand how it relates to the problem

4. $
log_{(\frac{1}{3})}\frac{1}{27} = 3
$

$
log_{(\frac{1}{4})}256 = -4
$