Q. 64 - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation $3^{-x}=81$

and verify your results using a graphing utility.

Step-by-Step Solution

Answer

Required solution set is {-4}. 

Step 1. Given information

$3^{-x}=81$

Step 2. Calculations

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

Step 3. Graphing solution

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

Hence the required solution set is {-4}.