Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 368: 33

Answer

$x=\dfrac{\log4}{\log5-\log4}\approx6.212567$

Work Step by Step

$5^{x}=4^{x+1}$ Apply $\log$ to both sides of the equation: $\log5^{x}=\log4^{x+1}$ The exponents $x$ and $x+1$ can be taken down to multiply in front of their respective logarithms: $x\log5=(x+1)\log4$ Solve for $x$: $x\log5=x\log4+\log4$ $x\log5-x\log4=\log4$ $x(\log5-\log4)=\log4$ $x=\dfrac{\log4}{\log5-\log4}\approx6.212567$
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