Precalculus Examples

$\log_{6} ({(\frac{z}{36})}^{4})$

Step 1

Expand $\log_{6} ({(\frac{z}{36})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{6} (\frac{z}{36})$

Step 2

Rewrite $\log_{6} (\frac{z}{36})$ as $\log_{6} (z) - \log_{6} (36)$ .

$4 (\log_{6} (z) - \log_{6} (36))$

Step 3

Logarithm base $6$ of $36$ is $2$ .

$4 (\log_{6} (z) - 1 \cdot 2)$

Step 4

Multiply $- 1$ by $2$ .

$4 (\log_{6} (z) - 2)$

Step 5

Apply the distributive property.

$4 \log_{6} (z) + 4 \cdot - 2$

Step 6

Multiply $4$ by $- 2$ .

$4 \log_{6} (z) - 8$