Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Review: 78

Answer

-.09

Work Step by Step

We are given that $log_{b}2=.36$ and that $ log_{b}5=.83$. The quotient property of logarithms tells us that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$). Therefore, $log_{b}\frac{4}{5}= log_{b}\frac{2^{2}}{5}=log_{b}2^{2}-log_{b}5$. The power property of logarithms tells us that $log_{b}x^{r}=r log_{b}x$ (where x and b are positive real numbers, $b\ne1$, and r is a real number). Therefore, $log_{b}2^{2}-log_{b}5=2log_{b}2-log_{b}5=2\times.36-.83=-.09$
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