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: 31

Answer

(a) $x=\frac{\ln\frac{50}{3}}{\ln 4}$ (b) $x\approx 2.029447$

Work Step by Step

(a) We need to solve: $4^{x}+2^{1+2x}=50$ $(2^2)^x+2^{1+2x}=50$ $2^{2x}(1+2^1)=50$ $2^{2x}(3)=50$ $2^{2x}=\frac{50}{3}$ 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): $x \ln2^2 = \ln 50-\ln 3=\ln\frac{50}{3}$ $x=\frac{\ln\frac{50}{3}}{\ln 4}$ (b) We solve using a calculator: $x\approx 2.029447$
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