College Algebra (6th Edition)

Published by Pearson

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3: 50

Answer

$log(xy^{7})$

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, $log(x)+7log(y)=log(x)+log(y^{7})$. Based on the product rule of logarithms, we know that $log_{b}(MN)=log_{b}M+log_{b}N$ (for $M\gt0$ and $N\gt0$). Therefore, $log(x)+log(y^{7})=log(xy^{7})$. In this case, the given logarithm is a common logarithm, which has an understood base of 10.

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