Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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