Expand the Logarithmic Expression log base 2 of (x^2-4)/(x^3)

$\log_{2} (\frac{x^{2} - 4}{x^{3}})$

Rewrite $\log_{2} (\frac{x^{2} - 4}{x^{3}})$ as $\log_{2} (x^{2} - 4) - \log_{2} (x^{3})$ .

$\log_{2} (x^{2} - 4) - \log_{2} (x^{3})$

Expand $\log_{2} (x^{3})$ by moving $3$ outside the logarithm.

$\log_{2} (x^{2} - 4) - (3 \log_{2} (x))$

Multiply $3$ by $- 1$ .

$\log_{2} (x^{2} - 4) - 3 \log_{2} (x)$