Precalculus Examples

$\ln (\frac{v (x - 2)}{y^{3} z^{3}})$

Step 1

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

$\ln (v (x - 2)) - \ln (y^{3} z^{3})$

Step 2

Rewrite $\ln (y^{3} z^{3})$ as $\ln (y^{3}) + \ln (z^{3})$ .

$\ln (v (x - 2)) - (\ln (y^{3}) + \ln (z^{3}))$

Step 3

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

$\ln (v (x - 2)) - (3 \ln (y) + \ln (z^{3}))$

Step 4

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

$\ln (v (x - 2)) - (3 \ln (y) + 3 \ln (z))$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\ln (v (x - 2)) - (3 \ln (y)) - (3 \ln (z))$

Step 5.2

Multiply $3$ by $- 1$ .

$\ln (v (x - 2)) - 3 \ln (y) - (3 \ln (z))$

Step 5.3

Multiply $3$ by $- 1$ .

$\ln (v (x - 2)) - 3 \ln (y) - 3 \ln (z)$