Intermediate Algebra (6th Edition)

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

Chapter 9 - Review: 77



Work Step by Step

We are given that $log_{b}2=.36$ and that $ log_{b}5=.83$. The product property of logarithms tells us that $log_{b}xy=log_{b}x+log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$). Therefore, $log_{b}50= .log_{b}(2\times25)=.log_{b}(2\times5^{2})=log_{b}2+log_{b}5^{2}$. 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, $log_{b}2+log_{b}5^{2}=log_{b}2+2log_{b}5=.36+2(.83)=2.02$
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