Algebra Examples

$\ln (\frac{3 x^{2}}{7 y})$

Step 1

Rewrite $\ln (\frac{3 x^{2}}{7 y})$ as $\ln (3 x^{2}) - \ln (7 y)$ .

$\ln (3 x^{2}) - \ln (7 y)$

Step 2

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

$\ln (3) + \ln (x^{2}) - \ln (7 y)$

Step 3

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

$\ln (3) + 2 \ln (x) - \ln (7 y)$

Step 4

Rewrite $\ln (7 y)$ as $\ln (7) + \ln (y)$ .

$\ln (3) + 2 \ln (x) - (\ln (7) + \ln (y))$

Step 5

Apply the distributive property.

$\ln (3) + 2 \ln (x) - \ln (7) - \ln (y)$