Q. 68 - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation $5^{x+3}=\frac{1}{5}$

and verify your results using a graphing utility.

Step-by-Step Solution

Answer

 Required solution set is {-4}. 

Step 1. Given information

$5^{x+3}=\frac{1}{5}$

Step 2. Calculations

$$\begin{gathered} 5^{x+3}=\frac{1}{5} \\ {5}^{x+3}=5^{-1} if a^u=a^v then u=v \\ x+3=-1 \\ x=-4 \end{gathered}$$

Step 3. Graphing solution

Graph  $y= 5^{x+3}$and y =1/5 intersect at (-4,0.2)

Hence the required solution set is {-4}.