Question

Solve the equation${\left(\frac{1}{4}\right)}^x=\frac{1}{64}$

and verify your results using a graphing utility.

Short answer

Required solution set is {3}.

Step-by-step solution

Step 1. Given information   

${\left(\frac{1}{4}\right)}^x=\frac{1}{64}$

Step 2. Calculations 

$$\begin{gathered} {\left(\frac{1}{4}\right)}^x=\frac{1}{64} \\ {4}^{-x}=4^{-3}if{a}^u=a^{v}thenu=v \\ x=3 \end{gathered}$$

Step 3. Graphing solution   

Graph $y=4^{-x}$and y =1/64 intersect at (3,0.015625)

Hence the required solution set is {3}.