Question

Evaluate${\log }_4\frac{1}{64}$

Short answer

The answer of the expression${\log }_4\frac{1}{64}=-3$

Step-by-step solution

Step 1. Given 

An expression is given as${\log }_4\frac{1}{64}$

Step 2. Calculation

Let the expression be $x$,

${\log }_4\frac{1}{64}=x$

Convert into exponential form and simplify,

$$\begin{gathered} 4^x=\frac{1}{64} \\ {4}^x=\frac{1}{4^3} \\ {4}^x=4^{-3} \\ x=-3 \end{gathered}$$