Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $- 1$ by $2$ .

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