Expand the Logarithmic Expression Expand log of (3x)/(2y)

Expand $\log (\frac{3 x}{2 y})$

Rewrite $\log (\frac{3 x}{2 y})$ as $\log (3 x) - \log (2 y)$ .

$\log (3 x) - \log (2 y)$

Rewrite $\log (3 x)$ as $\log (3) + \log (x)$ .

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

Rewrite $\log (2 y)$ as $\log (2) + \log (y)$ .

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

Apply the distributive property.

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