Answer
$x=1$.
Work Step by Step
$2^x\cdot5=10^x\\2^x\cdot5=(2\cdot5)^x\\2^x\cdot5=2^x5^x\\5=5^x\\5^1=5^x.$
We know that $a^x=a^y\longrightarrow x=y$ if $a\ne1,\ne-1$.
Hence here $x=1$.
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 - Chapter Review - Review Exercises - Page 346: 41
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