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: 26


(a) $x=-\frac{100\log 2}{\log 5}$ (b) $x\approx -43.067656$

Work Step by Step

(a) We need to solve: $5^{-x/100}=2$ We take the log of both sides and use log rules to simplify: $\log 5^{-x/100}=\log 2$ $-\frac{x}{100}\log 5=\log 2$ $-\frac{x}{100}=\frac{\log 2}{\log 5}$ $x=-\frac{100\log 2}{\log 5}$ (b) We solve using a calculator: $x\approx -43.067656$
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