Precalculus Examples

$\ln (\frac{3 x^{2}}{e})$

Rewrite $\ln (\frac{3 x^{2}}{e})$ as $\ln (3 x^{2}) - \ln (e)$ .

$\ln (3 x^{2}) - \ln (e)$

The natural logarithm of $e$ is $1$ .

$\ln (3 x^{2}) - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$\ln (3 x^{2}) - 1$

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

$\ln (3) + \ln (x^{2}) - 1$

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

$\ln (3) + 2 \ln (x) - 1$