Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.2 - Exponential Functions - 9.2 Exercises: 29

Answer

$x=\frac{3}{2}$

Work Step by Step

We are given the equation $100^{x}=1000$. First, we must write both sides using the same base. $((10)^{2})^{x}=10^{2x}=10^{3}$ Next, we must take the natural log of both sides. $ln(10^{2x})=ln(10^{3})$ $2xln(10)=3ln(10)$ Divide both sides by $ln(10)$. $2x=3$ Divide both sides by 2. $x=\frac{3}{2}$
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