Question

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

and verify your results using a graphing utility.

Short answer

Required solution set is {-4}.

Step-by-step solution

Step 1. Given information     

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

Step 2. Calculations   

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

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}.