Answer
$\displaystyle \log_{16}4=\frac{1}{2}$
Work Step by Step
$\log_{b}x=y $ is equivalent to $ b^{y}=x $
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$\log_{16}4=y \quad $ is equivalent to $ \quad 16^{y}=4$.
Now, since $4^{2}=16,$ it follows that $16^{1/2}=(4^{2})^{1/2}=4$,
meaning that $ y=\displaystyle \frac{1}{2}$
and $\displaystyle \log_{16}4=\frac{1}{2}$
