Answer
$x=8$
Work Step by Step
$2^{x-5}=8
\\2^{x-5}=2^3$
We know that if $a^b=a^c$ and $a\ne0,1,-1$, then $b=c.$
Hence,
$2^{x-5}=2^3\longrightarrow x-5=3$,
Add $5$ to both sides to obtain:
$x-5+5=3+5\\
x=8$.
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 41
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