# How do you evaluate the expression log_4(16^x)?

${\log}_{4} \left({16}^{x}\right) = 2 x .$
${\log}_{4} \left({16}^{x}\right)$
$= x \cdot {\log}_{4} \left(16\right)$
$= x \cdot \log \frac{16}{\log} 4$
$= x \cdot \log {4}^{2} / \log 4 = 2 x \cdot \log \frac{4}{\log} 4 = 2 x \cdot 1 = 2 x .$ (answer).