# calculus review sheet - logs

• Aug 15th 2008, 06:51 PM
apm
calculus review sheet - logs
i can't use a calculator
solve for x:

log3x^2=2log34 - 4log35

i know that properties of logarithms but i'm not sure how i should use them to solve for x

also how do you subtract logs of different bases
simplify:
2log49 - log23

i appreciate any help
• Aug 15th 2008, 07:00 PM
Prove It
Quote:

Originally Posted by apm
solve for x:

log3x^2=2log34 - 4log35

i know that properties of logarithms but i'm not sure how i should use them to solve for x

also how do you subtract logs of different bases
simplify:
2log49 - log23

i appreciate any help

You can't subtract logs of different bases, as they're unlike terms. It's like asking what $\displaystyle x-y$ is...

But to answer your first question, to solve for x in this case you have to get both sides to be of the form $\displaystyle \log_3$ something...

$\displaystyle \log_3x^2=2\log_34-4\log_35$
$\displaystyle \log_3x^2=\log_34^2-\log_35^4$
$\displaystyle \log_3x^2=\log_3(\frac{4^2}{5^4})$
$\displaystyle \log_3x^2=\log_3(\frac{4^2}{25^2})$
$\displaystyle x^2=\frac{4^2}{25^2}$
$\displaystyle x=\pm\frac{4}{25}$
• Aug 15th 2008, 07:34 PM
apm
thank you!