Statement
The logarithm of a power is the same of the exponent multiplied by that logarithm:
$$ \log_a(b^c) = c * \log_a(b) $$
Proof
Let $ x = \log_a(b) $. Now rewrite it as a power.
$$ a^x = b $$
Raise both sides to the power $ c $ and multiply the exponents.
$$ (a^x)^c = b^c $$
$$ a^{cx} = b^c $$
Take the logarithm with base $ a $ on both sides. Since $ \log_a $ and $ a^{...} $ are inverse operations, they cancel.
$$ \log_a(a^{cx}) = \log_a(b^c) $$
$$ c * x = \log_a(b^c) $$
Finally, re-substitue $ x $ and flip the equation.
$$ c * \log_a(b) = \log_a(b^c) $$
$$ \log_a(b^c) = c * \log_a(b) $$