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: 33


(a) $x=\frac{\log 4}{\log\frac{5}{4}}$ (b) $x\approx 6.212567$

Work Step by Step

(a) We need to solve: $5^{x}=4^{x+1}$ We take the log of both sides and use log rules to simplify: $\log 5^{x}=\log 4^{x+1}$ $x \log5 =(x+1) \log4$ $x \log5 =x\log 4+\log 4$ $x\log 5-x \log4 =\log 4$ $x(\log 5-\log 4)=\log 4$ $x=\frac{\log 4}{\log\frac{5}{4}}$ (b) We solve using a calculator: $x\approx 6.212567$
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