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: 31

Answer

$x=7$

Work Step by Step

We are given the equation $16^{2x+1}=64^{x+3}$. First, we must write both sides using the same base. $((4)^{2})^{2x+1}=4^{4x+2}$ $((4)^{3})^{x+3}=4^{3x+9}$ So, $4^{4x+2}=4^{3x+9}$. Next, we must take the natural log of both sides. $ln(4^{4x+2})=ln(4^{3x+9})$ $(4x+2)ln(4)=(3x+9)ln(4)$ Divide both sides by $ln(4)$. $4x+2=3x+9$ Subtract $3x$ from both sides. $x+2=9$ Subtract 2 from both sides. $x=7$
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