Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.3 Logarithmic Functions - 4.3 Exercises - Page 446: 91

Answer

$log_5(\frac{5^{1/3}}{m^{1/3}})$ or $log_5(\sqrt[3] {\frac{5}{m}})$

Work Step by Step

$-\frac{2}{3}log_5(5m^2)+\frac{1}{2}log_5(25m^2)=log_5(5m^2)^{-2/3}+log_5(5m)=log_5(5^{1/3}m^{-1/3})=log_5(\frac{5^{1/3}}{m^{1/3}})=log_5(\sqrt[3] {\frac{5}{m}})$
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