Answer
$$ x=6.$$
Work Step by Step
We have
$$ (\sqrt{5})^{x}=125 \Longrightarrow 5^{\frac{x}{2}}=5^3. $$
Since the bases are equal, then the exponents are equal and hence we get
$$\frac{x}{2}=3\Longrightarrow x=6.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 6
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