Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.3 Logarithmic Functions - 6.3 Exercises - Page 426: 6


(a) $2$ (b) $-3$

Work Step by Step

(a) Use logarithmic base formulas $\log_{b}x=\frac{log x}{log b}$ $\log_{1.5}2.25=\frac{log (2.25)}{log (1.5)}$ Thus, $\frac{log (2.25)}{log (1.5)}=\frac{log (1.5)^{2}}{log (1.5)}=2$ (b) Use logarithmic properties, $logx+logy=log(xy)$, $y logx=logx^{y}$ and $log x-log y=log(\frac{x}{y})$ $\log_{5}4-\log_{5}500=log_{5}(\frac{4}{500})=log_{5}(5^{-3})=-3$
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