Answer
$x=\frac{b}{a}$
Work Step by Step
Given that $2^a=5$ and $2^b=7$, we have
$$
\begin{aligned}
5^x & =7 \\
\left(2^a\right)^x & =2^b \\
2^{a x} & =2^b \\
a x & =b \\
x & =\frac{b}{a} .
\end{aligned}
$$
so $x=\frac{b}{a}$
Functions Modeling Change: A Preparation for Calculus, 5th Edition
by Connally, Eric; Hughes-Hallett, Deborah; Gleason, Andrew M.; Cheifetz, Phil C.
Published by
Wiley
ISBN 10:
1118583191
ISBN 13:
978-1-11858-319-7
Chapter 4 - Exponential Functions - Exercises to Skills for Chapter 4 - Page 186: 81
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