Precalculus Examples

$\log_{6} ({(8^{3} \cdot 11)}^{2})$

Step 1

Expand $\log_{6} ({(8^{3} \cdot 11)}^{2})$ by moving $2$ outside the logarithm.

$2 \log_{6} (8^{3} \cdot 11)$

Step 2

Raise $8$ to the power of $3$ .

$2 \log_{6} (512 \cdot 11)$

Step 3

Multiply $512$ by $11$ .

$2 \log_{6} (5632)$

Step 4

Rewrite $\log_{6} (5632)$ as $\log_{6} (2^{9} \cdot 11)$ .

$2 \log_{6} (2^{9} \cdot 11)$

Step 5

Rewrite $\log_{6} (2^{9} \cdot 11)$ as $\log_{6} (2^{9}) + \log_{6} (11)$ .

$2 (\log_{6} (2^{9}) + \log_{6} (11))$

Step 6

Expand $\log_{6} (2^{9})$ by moving $9$ outside the logarithm.

$2 (9 \log_{6} (2) + \log_{6} (11))$

Step 7

Apply the distributive property.

$2 (9 \log_{6} (2)) + 2 \log_{6} (11)$

Step 8

Multiply $9$ by $2$ .

$18 \log_{6} (2) + 2 \log_{6} (11)$