Precalculus Examples

$\ln (\frac{6 (x^{2})}{y^{4}})$

Step 1

Rewrite $\ln (\frac{6 (x^{2})}{y^{4}})$ as $\ln (6 (x^{2})) - \ln (y^{4})$ .

$\ln (6 (x^{2})) - \ln (y^{4})$

Step 2

Expand $\ln (y^{4})$ by moving $4$ outside the logarithm.

$\ln (6 (x^{2})) - (4 \ln (y))$

Step 3

Multiply $4$ by $- 1$ .

$\ln (6 (x^{2})) - 4 \ln (y)$

Step 4

Multiply $6$ by $x^{2}$ .

$\ln (6 x^{2}) - 4 \ln (y)$

Step 5

Rewrite $\ln (6 x^{2})$ as $\ln (6) + \ln (x^{2})$ .

$\ln (6) + \ln (x^{2}) - 4 \ln (y)$

Step 6

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

$\ln (6) + 2 \ln (x) - 4 \ln (y)$

Step 7

Simplify each term.

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Step 7.1

Rewrite $\ln (6)$ as $\ln (2 (3))$ .

$\ln (2 (3)) + 2 \ln (x) - 4 \ln (y)$

Step 7.2

Rewrite $\ln (2 (3))$ as $\ln (2) + \ln (3)$ .

$\ln (2) + \ln (3) + 2 \ln (x) - 4 \ln (y)$