College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.5 - Exponential and Logarithmic Equations - 4.5 Exercises - Page 446: 23

Answer

$x\approx3.0444$

Work Step by Step

Given Expression $3(2)^{x+2}+1=100$ Subtract 1 from both sides. $3(2)^{x+2}=99$ Divide both sides. $2^{x+2}=33$ Take log of both sides. $\log2^{x+2}=\log33$ Power Rule of logarithms. $(x+2)\log2=\log33$ Solve for $x$. $x=(\frac{\log33}{\log2})-2$ $x\approx3.0444$
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