Find the logarithm of $\dfrac{1}{16}$ to the base 4.

Let,

$\Rightarrow \text{log}_{(4)} \space \dfrac{1}{16} = x \\[1em] \Rightarrow \dfrac{1}{16} = 4^x\\[1em] \Rightarrow \dfrac{1}{4^2} = 4^x \\[1em] \Rightarrow 4^x = 4^{-2} \\[1em] \Rightarrow x = -2.$

Hence, required value = -2.