College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4: 42

Answer

$x\approx0.08$

Work Step by Step

Find the natural log of both sides and then pull out the exponents on both sides. Then solve for $x$. $7^{2x+1}=3^{x+2}$ $(2x+1)\ln(7)=(x+2)\ln(3)$ $\frac{2x+1}{x+2}=\frac{\ln(3)}{\ln(7)}$ $\frac{2x+1}{x+2}=0.56$ $0.56(x+2)=2x+1$ $0.56x+1.12=2x+1$ $1.12=1.44x+1$ $0.12=1.44x$ $x\approx0.08$
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