Q. 66 - Precalculus Enhanced with Graphing Utilities

Question

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

and verify your results using a graphing utility.

Step-by-Step Solution

Answer

Required solution set is {3}.  

Step 1. Given information

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

Step 2. Calculations

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

Step 3. Graphing solution

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

Hence the required solution set is {3}.