Answer
$x=1$
Work Step by Step
We know that $a^b=a^c\longrightarrow b=c$ if $a\ne1,a\ne-1$ (which applies here).
Hence here $2^x\cdot5=10^x\\2^x\cdot5=(2\cdot5)^x\\2^x\cdot5=2^x\cdot5^x\\5=5^1=5^x\\x=1$
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 6 - Review Exercises - Page 500: 41
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