Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.6 - Properties of Logarithms - Exercise Set: 45

Answer

$\frac{1}{2}log_{b}7+\frac{1}{2}log_{b}x$

Work Step by Step

We know that $log_{b}xy=log_{b}x+log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$). Therefore, $log_{b}\sqrt 7x=log_{b}(7^{\frac{1}{2}}x^{\frac{1}{2}})=log_{b}7^{\frac{1}{2}}+log_{b}x^{\frac{1}{2}}$. We know that $log_{b}x^{r}=rlog_{b}x$ (where $x$ and $b$ are positive real numbers, $b\ne1$, and $r$ is a real number). Therefore, $log_{b}7^{\frac{1}{2}}+log_{b}x^{\frac{1}{2}}=\frac{1}{2}log_{b}7+\frac{1}{2}log_{b}x$.
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