# Math Help - Logarithms...ugh

1. ## Logarithms...ugh

I need to rearrange this:
log x + log y = z

to prove that
z = log xy

I've managed to get to:
x = 10(raised to) z - log y

Don't know if I'm going in the right direction, or where to go from there

2. This is a rule of logarithms:

$\log {a} + \log {b} = \log {ab}$

Pretty straight forward.

3. $\log_b(xy) = \log_b(x) + \log_b(y) \!\,$ because $b^x \cdot b^y = b^{x + y} \!\,$
From Wikipedia

In detail:

$b^{\log_bx}=x,\enspace b^{\log_by}=y\rightarrow b^{\log_bx+\log_by}=xy=b^{\log_b(xy)}$