Recall the following two facts:

Logarithms and Exponentials are inverses of each other. (Of course they need to have the same base.)
Exponential functions are just powers and logarithms are just exponents.
For the following proposed identities enter T if they are true, and F if they are false. We assume that the expressions involved make sense. For example any base is positive and not equal to 1, and logarithms are taken only of positive numbers.

$\log_a(uv) = \log_a u + \log_a v.$
$\log_a(u+v) = (\log_a u) (\log_a v).$
$\log_a\left(\frac{u}{v}\right) = \log_a u - \log_a v.$
$\log_a(u-v) = \frac{\log_a u}{\log_a v}.$
$\log_a\left(u^v\right) = (\log_a u) (\log_a v).$
$\log_a\left(u^v\right) = u (\log_a v).$
$\log_a\left(u^v\right) = v (\log_a u).$