Expand the Logarithmic Expression log base a of (x^2)/(yz^3)

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

Step 1

Rewrite $\log_{a} (\frac{x^{2}}{y z^{3}})$ as $\log_{a} (x^{2}) - \log_{a} (y z^{3})$ .

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

Step 2

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

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

Step 3

Rewrite $\log_{a} (y z^{3})$ as $\log_{a} (y) + \log_{a} (z^{3})$ .

$2 \log_{a} (x) - (\log_{a} (y) + \log_{a} (z^{3}))$

Step 4

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

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

Step 5

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

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