Expand the Logarithmic Expression log of (3x^2)/12

$\log (\frac{3 x^{2}}{12})$

Step 1

Rewrite $\log (\frac{3 x^{2}}{12})$ as $\log (3 x^{2}) - \log (12)$ .

$\log (3 x^{2}) - \log (12)$

Step 2

Rewrite $\log (12)$ as $\log (2^{2} \cdot 3)$ .

$\log (3 x^{2}) - \log (2^{2} \cdot 3)$

Step 3

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

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

Step 4

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

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

Step 5

Apply the distributive property.

$\log (3 x^{2}) - (2 \log (2)) - \log (3)$

Step 6

Multiply $2$ by $- 1$ .

$\log (3 x^{2}) - 2 \log (2) - \log (3)$

Step 7

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

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

Step 8

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

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

Step 9

Subtract $\log (3)$ from $\log (3)$ .

$0 + 2 \log (x) - 2 \log (2)$

Step 10

Add $0$ and $2 \log (x)$ .

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