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 466: 63


The solution set is $\{\log_{5}4\}$ or $\{0.861\}$

Work Step by Step

... $\quad 25x=(5^{2})^{x}=(5^{x})^{2}$ ... Substitute $t=5^{x}$ (t is positive) ... the equation becomes $t^{2}-8t+16=0 \quad $...recognize a square of a difference $(t-4)^{2}=0$ $t=4 \quad $... bring back x $5^{x}=4 \quad $...Apply$: \quad \log_{5}(...)$ $x=\log_{5}4\approx 0.861$ The solution set is $\{\log_{5}4\}$ or $\{0.861\}$
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