College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3: 55

Answer

$ln(\frac{x^{5}}{y^{2}})$

Work Step by Step

According to the power rule of logarithms, we know that $log_{b}M^{p}=plog_{b}M$ (when $b$ and $M$ are positive real numbers, $b\ne1$, and $p$ is any real number). Therefore, $5ln(x)-2ln(y)=ln(x^{5})-ln(y^{2})$. Based on the quotient rule of logarithms, we know that $log_{b}(\frac{M}{N})=log_{b}M-log_{b}N$ (where $b$, $M$, and $N$ are positive real numbers and $b\ne1$). Therefore, $ ln(x^{5})-ln(y^{2})=ln(\frac{x^{5}}{y^{2}})$. In this case, the given logarithm is a natural logarithm with an understood base of $e$.
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