Precalculus Examples

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

Step 1

Expand $\ln ({(\frac{x + 2}{y z^{3}})}^{2})$ by moving $2$ outside the logarithm.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $3$ by $- 1$ .

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

Step 6

Apply the distributive property.

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

Step 7

Simplify.

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Step 7.1

Multiply $- 1$ by $2$ .

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

Step 7.2

Multiply $- 3$ by $2$ .

$2 \ln (x + 2) - 2 \ln (y) - 6 \ln (z)$