# What is x if log_4(16x) = 1/2?

Oct 22, 2015

$\frac{1}{8}$
According to the definition of logarithm ${\log}_{4} \left(16 x\right) = \frac{1}{2}$ is equal to ${4}^{\frac{1}{2}}$=$16 x$
${4}^{\frac{1}{2}} = 2$ so you have $2 = 16 x$
$\frac{2}{16} = x$ or $x = \frac{1}{8}$