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: 23

Answer

(a) $x=\frac{5}{7}-\frac{\ln 15}{7\ln 2}$ (b) $x\approx 0.156158$

Work Step by Step

(a) We need to solve: $2^{5-7x}=15$ We take the natural log of both sides and use log rules to simplify: $(5-7x) \ln2 = \ln 15$ $5-7x=\frac{\ln 15}{\ln 2}$ $5-\frac{\ln 15}{\ln 2}=7x$ $x=\frac{5}{7}-\frac{\ln 15}{7\ln 2}$ (b) We solve using a calculator: $x\approx 0.156158$
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