Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.5 Logarithmic Functions - 2.5 Exercises: 35

Answer

$3a+2c+1$

Work Step by Step

$72=8\cdot 9=2^{3}\cdot 3^{2}$ $\log_{b}(72b)=\log_{b}(2^{3}\cdot 3^{2}\cdot b)$ ... apply $\ \ \log_{a}xy=\log_{a}x+\log_{a}y$ $=\log_{b}2^{3}+\log_{b}3^{2}+\log_{b}b$ ... apply $\ \ \log_{a}x^{r}=r\log_{a}x$ ... apply $\ \ \log_{b}b=1$ $=3\log_{b}2+2\log_{b}3+1$ $=3a+2c+1$
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