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: 13

Answer

$2-ln(5)$

Work Step by Step

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 $b\ne1$). We know that $ln(x)$ is a natural logarithm with an understand base of $e$. Therefore, $ln(\frac{e^{2}}{5})=log_{e}e^{2}-ln(5)$. Based on the definition of the logarithmic function, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (for $x\gt0$ and $b\gt0$, $b\ne1$). Therefore, $log_{e}e^{2}=2$, because $(e)^{2}=e^{2}$. So, $log_{e}e^{2}-ln(5)=2-ln(5)$.
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