## Algebra: A Combined Approach (4th Edition)

Published by Pearson

# Chapter 12 - Section 12.6 - Properties of Logarithms - Exercise Set: 38

#### Answer

$5\log_{6}x-\dfrac{3}{4}\log_{6}x+3\log_{6}x=\log_{6}x^{29/4}$

#### Work Step by Step

$5\log_{6}x-\dfrac{3}{4}\log_{6}x+3\log_{6}x$ Take the numbers multiplying in front of each $\log$ as exponents: $\log_{6}x^{5}-\log_{6}x^{3/4}+\log_{6}x^{3}=...$ Combine $\log_{6}x^{5}-\log_{6}x^{3/4}$ as the $\log$ of a division: $...=\log_{6}\dfrac{x^{5}}{x^{3/4}}+\log_{6}x^{3}=...$ Combine $\log_{6}\dfrac{x^{5}}{x^{3/4}}+\log_{6}x^{3}$ as the $\log$ of a product and simplify: $...=\log_{6}\dfrac{x^{5}\cdot x^{3}}{x^{3/4}}=\log_{6}\dfrac{x^{8}}{x^{3/4}}=\log_{6}x^{29/4}$

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