Question

Solve the equation$3^{-x}=81$

and verify your results using a graphing utility.

Short answer

Required solution set is {-4}.

Step-by-step solution

Step 1. Given information 

$3^{-x}=81$

Step 2. Calculations 

$$\begin{gathered} 3^{-x}=81 \\ {3}^{-x}=3^{4}if{a}^u=a^{v}thenu=v \\ x=-4 \end{gathered}$$

Step 3. Graphing solution 

Graph $y=3^{-x}$and y =81 intersect at (-4,81)

Hence the required solution set is {-4}.