Precalculus Examples

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

Step 1

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

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

Step 2

Rewrite $\ln (z w^{2})$ as $\ln (z) + \ln (w^{2})$ .

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

Step 3

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

$\ln (x) - (\ln (z) + 2 \ln (w))$

Step 4

Simplify each term.

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Step 4.1

Apply the distributive property.

$\ln (x) - \ln (z) - (2 \ln (w))$

Step 4.2

Multiply $2$ by $- 1$ .

$\ln (x) - \ln (z) - 2 \ln (w)$