Q. 63 - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation $2^{-x}=16$

and verify your results using a graphing utility

Step-by-Step Solution

Answer

 Required solution set is {-4}. 

Step 1. Given information

$2^{-x}=16$

Step 2. Calculations

$$\begin{gathered} 2^{-x}=16 \\ {2}^{-x}=2^4 if a^u=a^v then u=v \\ x=-4 \end{gathered}$$

Step 3. Graphing solution

Graph  $y=2^{-x}$and $y=16$intersect at (-4,16).

Hence the required solution set is {-4}.