Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise - Page 463: 7


(a) $\log_{2}32= 5$ (b) $\log_{8}2= 0.3333$

Work Step by Step

(a) $\log_{2}32= \log_{2}(2^{5})$ Since, $logx^{y}=xlogy$ $\log_{2}32= \log_{2}(2^{5})$ Use logarithmic base formula $\log_{b}x=\frac{log x}{log b}$ $\log_{2}(2^{5}) =5\log_{2}2=5\times\frac{log 2}{log 2}$ Hence, $\log_{2}32= 5$ (b) Since, $\log_{b}x=\frac{log x}{log b}$ $\log_{8}2 =\frac{log 2}{log 8}$ Hence, $\log_{8}2= 0.3333$
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