College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 16


(a) $x=\frac{1}{2}+\frac{1}{2}\frac{\log 5}{\log 3}$ (b) $x\approx 1.232487$

Work Step by Step

(a) We need to solve: $3^{2x-1}=5$ We take the log of both sides and use log rules to simplify: $\log 3^{2x-1}=\log 5$ $(2x-1)\log 3=\log 5$ $2x-1=\frac{\log 5}{\log 3}$ $2x=1+\frac{\log 5}{\log 3}$ $x=\frac{1}{2}(1+\frac{\log 5}{\log 3})$ $x=\frac{1}{2}+\frac{1}{2}\frac{\log 5}{\log 3}$ (b) We solve using a calculator: $x\approx 1.232487$
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