Expand the Logarithmic Expression log base 4 of (3xyz)^2

$\log_{4} ({(3 x y z)}^{2})$

Step 1

Expand $\log_{4} ({(3 x y z)}^{2})$ by moving $2$ outside the logarithm.

$2 \log_{4} (3 x y z)$

Step 2

Rewrite $\log_{4} (3 x y z)$ as $\log_{4} (3 x y) + \log_{4} (z)$ .

$2 (\log_{4} (3 x y) + \log_{4} (z))$

Step 3

Rewrite $\log_{4} (3 x y)$ as $\log_{4} (3 x) + \log_{4} (y)$ .

$2 (\log_{4} (3 x) + \log_{4} (y) + \log_{4} (z))$

Step 4

Rewrite $\log_{4} (3 x)$ as $\log_{4} (3) + \log_{4} (x)$ .

$2 (\log_{4} (3) + \log_{4} (x) + \log_{4} (y) + \log_{4} (z))$

Step 5

Apply the distributive property.

$2 \log_{4} (3) + 2 \log_{4} (x) + 2 \log_{4} (y) + 2 \log_{4} (z)$