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: 10

Answer

(a) $log_{a}\frac{1}{a} =-1$ (b) $10^{(log_{10}4+log_{10}7)} =28$

Work Step by Step

(a) Use logarithmic base formulas $\log_{b}x=\frac{log x}{log b}$ and $\log b^{x}=x log b$ $log_{a}\frac{1}{a}=log_{a}a^{-1}$ $=-1 log_{a}a$ $=-1\times\frac{log a}{log a}$ $=-1$ Hence, $log_{a}\frac{1}{a} =-1$ (b) $10^{(log_{10}4+log_{10}7)}= 10^{log_{10}(4\times7)}$ $=10^{log_{10}(28)}$ Apply $\log b^{\log_{b}x}=x$ Hence, $10^{(log_{10}4+log_{10}7)} =28$
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