Question

Solve the equation$2^{-x}=16$

and verify your results using a graphing utility

Short answer

Required solution set is {-4}.

Step-by-step solution

Step 1. Given information 

$2^{-x}=16$

Step 2. Calculations 

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

Step 3. Graphing solution 

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

Hence the required solution set is {-4}.