# How do you calculate  log_16(3)?

Nov 8, 2016

$x = 0.3962$
Let ${\log}_{16} \left(3\right) = x$, then ${16}^{x} = 3$
or $x \log 16 = \log 3$
or $x = \log \frac{3}{\log} 16 = \frac{0.4771}{1.2041} = 0.3962$