Precalculus Examples

$\log_{2} (\frac{4 x^{3}}{x^{2} - 3 x - 18})$

Step 1

Rewrite $\log_{2} (\frac{4 x^{3}}{x^{2} - 3 x - 18})$ as $\log_{2} (4 x^{3}) - \log_{2} (x^{2} - 3 x - 18)$ .

$\log_{2} (4 x^{3}) - \log_{2} (x^{2} - 3 x - 18)$

Step 2

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

$\log_{2} (4) + \log_{2} (x^{3}) - \log_{2} (x^{2} - 3 x - 18)$

Step 3

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

$\log_{2} (4) + 3 \log_{2} (x) - \log_{2} (x^{2} - 3 x - 18)$

Step 4

Logarithm base $2$ of $4$ is $2$ .

$2 + 3 \log_{2} (x) - \log_{2} (x^{2} - 3 x - 18)$