Precalculus Examples

$(\ln (5^{- 3})) \ln^{3} (\frac{2}{9})$

Step 1

Expand $\ln (5^{- 3})$ by moving $- 3$ outside the logarithm.

$- 3 \ln (5) \ln^{3} (\frac{2}{9})$

Step 2

Rewrite $\ln (\frac{2}{9})$ as $\ln (2) - \ln (9)$ .

$- 3 \ln (5) {(\ln (2) - \ln (9))}^{3}$

Step 3

Rewrite $\ln (9)$ as $\ln (3^{2})$ .

$- 3 \ln (5) {(\ln (2) - \ln (3^{2}))}^{3}$

Step 4

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

$- 3 \ln (5) {(\ln (2) - (2 \ln (3)))}^{3}$

Step 5

Multiply $2$ by $- 1$ .

$- 3 \ln (5) {(\ln (2) - 2 \ln (3))}^{3}$