Logarithmic functions help.

Some of the questions are a bit ambiguous but seems like they involve the application of the chain rule which says:
$\left[f(g(x))\right]' = f'\left(g(x)\right) \cdot g'(x)$

For: $y = ln\left(\frac{2x-3}{x^{2}-4}\right)$
Let: $f(x) = ln(x) \quad \quad g(x) = \frac{2x - 3}{x^{2}-4}$

Applying the formula:
$\left[ ln\left(\frac{2x-3}{x^{2}-4}\right) \right]' = \underbrace{\frac{1}{g(x)}}_{(\ln x)' = \frac{1}{x}} \cdot \: \:g'(x)$
$= \frac{1}{\frac{2x - 3}{x^{2}-4}} \cdot \left(\frac{2x-3}{x^{2}-4}\right)'$
$= \frac{x^{2} - 4}{2x - 3} \cdot \underbrace{\left(\frac{2x-3}{x^{2}-4}\right)'}_{\mbox{Quotient Rule}}$

See if you can apply the chain rule to the other questions.