Precalculus Examples

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

Step 1

Expand $\ln ({(x^{4} \cdot y)}^{2})$ by moving $2$ outside the logarithm.

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

Step 2

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

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

Step 3

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

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $4$ by $2$ .

$8 \ln (x) + 2 \ln (y)$