Expand the Logarithmic Expression log base 3 of 81/((yz)^5)

$\log_{3} (\frac{81}{{(y z)}^{5}})$

Step 1

Rewrite $\log_{3} (\frac{81}{{(y z)}^{5}})$ as $\log_{3} (81) - \log_{3} ({(y z)}^{5})$ .

$\log_{3} (81) - \log_{3} ({(y z)}^{5})$

Step 2

Expand $\log_{3} ({(y z)}^{5})$ by moving $5$ outside the logarithm.

$\log_{3} (81) - (5 \log_{3} (y z))$

Step 3

Logarithm base $3$ of $81$ is $4$ .

$4 - (5 \log_{3} (y z))$

Step 4

Multiply $5$ by $- 1$ .

$4 - 5 \log_{3} (y z)$

Step 5

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

$4 - 5 (\log_{3} (y) + \log_{3} (z))$

Step 6

Apply the distributive property.

$4 - 5 \log_{3} (y) - 5 \log_{3} (z)$