Expand the Logarithmic Expression log of 6x^3yz

$\log (6 x^{3} y z)$

Step 1

Rewrite $\log (6 x^{3} y z)$ as $\log (6 x^{3} y) + \log (z)$ .

$\log (6 x^{3} y) + \log (z)$

Step 2

Rewrite $\log (6 x^{3} y)$ as $\log (6 x^{3}) + \log (y)$ .

$\log (6 x^{3}) + \log (y) + \log (z)$

Step 3

Rewrite $\log (6 x^{3})$ as $\log (6) + \log (x^{3})$ .

$\log (6) + \log (x^{3}) + \log (y) + \log (z)$

Step 4

Expand $\log (x^{3})$ by moving $3$ outside the logarithm.

$\log (6) + 3 \log (x) + \log (y) + \log (z)$

Step 5

Simplify each term.

Rewrite $\log (6)$ as $\log (2 (3))$ .

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

Rewrite $\log (2 (3))$ as $\log (2) + \log (3)$ .

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