Thread: calculus review sheet - logs

1. 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

2. 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 $x-y$ 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 $\log_3$ something...

$\log_3x^2=2\log_34-4\log_35$
$\log_3x^2=\log_34^2-\log_35^4$
$\log_3x^2=\log_3(\frac{4^2}{5^4})$
$\log_3x^2=\log_3(\frac{4^2}{25^2})$
$x^2=\frac{4^2}{25^2}$
$x=\pm\frac{4}{25}$

3. thank you!