Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Chapter Review - Review Exercises - Page 370: 42

Answer

$x=1$

Work Step by Step

Recall the rule that $a^m=a^n \longrightarrow m=n$ if $a\ne1,a\ne-1$ Applying this rule, we obtain: $(2^{x}) (5)=10^x \\ (2^x)(5) =(2 \cdot 5)^{x} \\ (2^x)(5)=2^{x} \cdot 5^x \\5^1 =5^x$ The base is the same, so their exponents can be equal. Therefore, we have: $x=1$
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