Question

How to expand this logarithm?

Answer 1

There is a division symbol, division is subtracted. Are you sure you have the problem stated clearly?
$ln( \frac{-5m-3}{ \sqrt{-4m-7} } )\\ \\ ln(-5m-3) - ln( (-4m-7)^{1/2} ) \\ \\ Power Rule \\ \\ ln(-5m-3) - \frac{1}{2} ln(-4m-7)$