Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $4$ by $- 1$ .

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

Step 4

Rewrite $\ln (4 x^{4})$ as $\ln (4) + \ln (x^{4})$ .

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

Step 5

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

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

Step 6

Simplify each term.

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Step 6.1

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

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

Step 6.2

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

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