College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.6 - Logarithmic and Exponential Equations - 6.6 Assess Your Understanding - Page 465: 38


$\{1+\sqrt[3]{2}\}$ or $\{2.260\}$

Work Step by Step

(*) For the equation to be defined, it must be true that $x \gt 1$ ...Apply$: \quad \log_{a}M^{r}=r\log_{a}M\quad $ $\log(x-1)=\log 2^{1/3}$ ...Apply$: \quad $If $\log_{a}M=\log_{a}N,$ then $M=N$ $x-1=2^{1/3}$ $x=1+\sqrt[3]{2}\approx 2.25992$ The solution satisfies (*), so the solution set is $\{1+\sqrt[3]{2}\}$ or $\{2.260\}$
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