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: 16

Answer

$x=5$

Work Step by Step

We are given the exponential equation $7^{\frac{x-2}{6}}=\sqrt7$. We can express each side using a common base and then solve for $x$. $7^{\frac{x-2}{6}}=7^{\frac{1}{2}}=\sqrt 7$ Take the natural log of both sides. $ln(7^{\frac{x-2}{6}})=ln(7^{\frac{1}{2}})$ $(\frac{x-2}{6})ln(7)=\frac{1}{2}ln(7)$ Divide both sides by $ln(7)$. $\frac{x-2}{6}=\frac{1}{2}$ Multiply both sides by 6. $x-2=3$ Add 2 to both sides. $x=5$
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