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: 28


(a) $x=\frac{\ln 45}{\ln 3}-1$ (b) $x\approx 2.464974$

Work Step by Step

(a) We need to solve: $2(5+3^{x+1})=100$ $5+3^{x+1}=\frac{100}{2}=50$ $3^{x+1}=50-5=45$ We take the log of both sides and use log rules to simplify (we choose the natural log, but any other base would work as well): $\ln 3^{x+1}=\ln 45$ $(x+1) \ln3 = \ln 45$ $x+1=\frac{\ln 45}{\ln 3}$ $x=\frac{\ln 45}{\ln 3}-1$ (b) We solve using a calculator: $x\approx 2.464974$
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