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: 15

Answer

$x=5$

Work Step by Step

We are given the exponential equation $6^{\frac{x-3}{4}}=\sqrt6$. We can express each side using a common base and then solve for $x$. $6^{\frac{x-3}{4}}=6^{\frac{1}{2}}=\sqrt 6$ Take the natural log of both sides. $ln(6^{\frac{x-3}{4}})=ln(6^{\frac{1}{2}})$ $(\frac{x-3}{4})ln(6)=\frac{1}{2}ln(6)$ Divide both sides by $ln(6)$. $\frac{x-3}{4}=\frac{1}{2}$ Multiply both sides by 4. $x-3=2$ Add 3 to both sides. $x=5$
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