Calculus Examples

$\ln ({(\frac{x^{2} - 2}{x^{3}})}^{2})$

Step 1

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

$2 \ln (\frac{x^{2} - 2}{x^{3}})$

Step 2

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

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

Step 3

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

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

Step 4

Multiply $3$ by $- 1$ .

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

Step 5

Apply the distributive property.

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

Step 6

Multiply $- 3$ by $2$ .

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