Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $3$ by $- 1$ .

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