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Q. 68

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Found in: Page 284

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Solve the equation ${5}^{x+3}=\frac{1}{5}$and verify your results using a graphing utility.

Required solution set is {-4}.

See the step by step solution

## Step 1. Given information

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

## Step 2. Calculations

${5}^{x+3}=\frac{1}{5}\phantom{\rule{0ex}{0ex}}{5}^{x+3}={5}^{-1}if{a}^{u}={a}^{v}thenu=v\phantom{\rule{0ex}{0ex}}x+3=-1\phantom{\rule{0ex}{0ex}}x=-4$

## 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}.
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