# Chapter 4 - Section 4.4 - Laws of Logarithms - 4.4 exercises: 58

$\log_a (\frac{bd^c}{s^r})$

#### Work Step by Step

$Combine$ $the$ $expresssion$: $\log_a b$ + $c$$\log_a d - r$$\log_a s$ Apply the Third Law of Logarithms for $c$$\log_a d and r$$\log_a s$ $c$$\log_a d = \log_a d^c r$$\log_a s$ = $\log_a s^r$ $\log_a b$ + $\log_a d^c$ - $\log_a s^r$ Apply the First Law of Logarithms for $\log_a b$ + $\log_a d^c$ $\log_a b$ + $\log_a d^c$ = $\log_a (b\times d^c)$ $\log_a (bd^c)$ - $\log_a s^r$ Apply the Second Law of Logarithms $\log_a (bd^c)$ - $\log_a s^r$ = $\log_a (\frac{bd^c}{s^r})$

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