Expand the Logarithmic Expression log base 7 of 5x^3yz^2

$\log_{7} (5 x^{3} y z^{2})$

Step 1

Rewrite $\log_{7} (5 x^{3} y z^{2})$ as $\log_{7} (5 x^{3} y) + \log_{7} (z^{2})$ .

$\log_{7} (5 x^{3} y) + \log_{7} (z^{2})$

Step 2

Rewrite $\log_{7} (5 x^{3} y)$ as $\log_{7} (5 x^{3}) + \log_{7} (y)$ .

$\log_{7} (5 x^{3}) + \log_{7} (y) + \log_{7} (z^{2})$

Step 3

Rewrite $\log_{7} (5 x^{3})$ as $\log_{7} (5) + \log_{7} (x^{3})$ .

$\log_{7} (5) + \log_{7} (x^{3}) + \log_{7} (y) + \log_{7} (z^{2})$

Step 4

Expand $\log_{7} (x^{3})$ by moving $3$ outside the logarithm.

$\log_{7} (5) + 3 \log_{7} (x) + \log_{7} (y) + \log_{7} (z^{2})$

Step 5

Expand $\log_{7} (z^{2})$ by moving $2$ outside the logarithm.

$\log_{7} (5) + 3 \log_{7} (x) + \log_{7} (y) + 2 \log_{7} (z)$