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: 15


(a) $x=1-\frac{\log 3}{\log 2}$ (b) $x\approx-0.584963$

Work Step by Step

(a) We need to solve: $2^{1-x}=3 $ We take the log of both sides and use log rules to simplify: $\log 2^{1-x}=\log 3$ $(1-x)\log 2=\log 3$ $1-x=\frac{\log 3}{\log 2}$ $x=1-\frac{\log 3}{\log 2}$ (b) We use a calculator: $x\approx-0.584963$
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