# Chapter 4 - Section 4.4 - Laws of Logarithms - 4.4 exercises: 35

$\log_5 3$ + 2$\log_5 x$ - 3$\log_5 y$

#### Work Step by Step

$Expand$ $the$ $expression$: $\log_5 \frac{3x^2}{y^3}$ Apply the Second Law of Logarithms $\log_5 \frac{3x^2}{y^3}$ = $\log_5 3x^2$ - $\log_5 y^3$ Apply the First Law of Logarithms to $\log_5 3x^2$ $\log_5 (3\times x^2)$ = $\log_5 3$ + $\log_5 x^2$ $\log_5 3x^2$ - $\log_5 y^3$ = $\log_5 3$ + $\log_5 x^2$ - $\log_5 y^3$ Apply the Third Law of logarithms to $\log_5 x^2$ and $\log_5 y^3$ $\log_5 x^2$ = 2$\log_5 x$ $\log_5 y^3$ = 3$\log_5 y$ $\log_5 3$ + $\log_5 x^2$ - $\log_5 y^3$ = $\log_5 3$ + 2$\log_5 x$ - 3$\log_5 y$

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