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 - Page 490: 40

Answer

$x\approx-10.25$

Work Step by Step

Find the natural log of both sides and then pull out the exponent to the left side. Then solve for $x$. $3^{\frac{x}{7}}=0.2$ $\frac{x}{7}\ln(3)=\ln(0.2)$ $\frac{x}{7}=\frac{\ln(0.2)}{\ln(3)}$ $x=7\times\frac{\ln(0.2)}{\ln(3)}$ $x\approx-10.25$
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