Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Apply the distributive property.

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

Step 5

Add $\ln (x)$ and $2 \ln (x)$ .

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