Calculus (3rd Edition)

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


$$ x=6.$$

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 $$\frac{x}{2}=3\Longrightarrow x=6.$$
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