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: 9

Answer

$log_{10}x-2$

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 $log(x)$ is a common logarithm with an understand base of 10. Therefore, $log(\frac{x}{100})=log_{10}x-log_{10}100$. 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, $log_{10}100=2$, because $10^{2}=100$. So, $log_{10}x-log_{10}100=log_{10}x-2$.
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