3^x = 5^y what is x/y ? Plz help . I'm terrible with Logs

Question

anonymous · Answer

Bah, logs with different bases . . .
Gimme a sec to remember how to do this.

anonymous · Answer

Ok, got it.
Take $\large log_3$ of both sides.

anonymous · Answer

Then you can use the logarithm power rule.

3psilon · Answer

Do you mind working please? @CliffSedge . I'm a little rusty on the rules

anonymous · Answer

Oh, I suppose so. It's pretty easy..

Given $\large 3^x = 5^y$

$\large log_3$ both sides

$\large log_3(3^x) = log_3(5^y)$

$\large x = 3^x = log_3(5^y)$

Understand so far?

anonymous · Answer

*oops, never mind that = "3x" in the last line. I thought I deleted that.

3psilon · Answer

I'm sorta catching on

anonymous · Answer

Should be $\large x=log_3(5^y)$

anonymous · Answer

Do you see that $\large log_3(3^x)=x$ ?

anonymous · Answer

The logarithm function tells you what the exponent is on that base.

anonymous · Answer

So, since a logarithm is an exponent, and if you have a power-to-a-power, you multiply exponents,

$\large log_3(5^y)=y log_3(5)$ .

I think you can get the rest from here.

zepdrix · Answer

|dw:1351900584391:dw|
Still having some trouble pimp or you figured this one out already.
Figured I'd throw my 2 cents just in case :D
Sorry that it's a little bit messy, hopefully you can follow it.
The asterisks are log rules.