Answer
$ln5+ln(x)+\frac{1}{2}ln(1+3x)-3ln(x-4)$
Work Step by Step
$ln\frac{5x\sqrt {1+3x}}{(x-4)^3}=ln(5x)+ln(\sqrt {1+3x})-ln(x-4)^3=ln5+ln(x)+\frac{1}{2}ln(1+3x)-3ln(x-4)$
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