# Math Help - Properties of Logarithms

1. ## Properties of Logarithms

$
2^{log_{2}5} - 3log_{5}(^{3}\sqrt{5})
$

Thanks for the help!

2. Hint: logs and exponents "undo" each other

$log_b\ (b^{(stuff)})=stuff$ and also $b^{log_b(stuff)}=stuff$

The key is that you need the bases the same.

3. I kind of understand what you're saying, but I'm not really getting the whole problem in general.

So, $2^{log_{2}5}$ equals 5?
What happens with $3log_{5}(^{3}\sqrt{5})
$
?

4. Originally Posted by juicysharpie
I kind of understand what you're saying, but I'm not really getting the whole problem in general.

So, $2^{log_{2}5}$ equals 5?
Yes.

What happens with $3log_{5}(^{3}\sqrt{5})
$
?
This one is more complicated.

Is it more clear if you write it this way: $3\ [\ log_{5}(5^{1/3})\ ]$, so ultimately it becomes 1, after multiplying the 3 through?

5. Oh, I see! Thanks for the help! I'm studying for a test, but I haven't done this stuff in awhile, so I'm a little rusty. Thanks again!

6. You're Welcome!! Good luck on the test!