Precalculus Examples

$\log_{6} (8^{2} \cdot 7^{2})$

Step 1

Rewrite $\log_{6} (8^{2} \cdot 7^{2})$ as $\log_{6} (8^{2}) + \log_{6} (7^{2})$ .

$\log_{6} (8^{2}) + \log_{6} (7^{2})$

Step 2

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

$2 \log_{6} (8) + \log_{6} (7^{2})$

Step 3

Expand $\log_{6} (7^{2})$ by moving $2$ outside the logarithm.

$2 \log_{6} (8) + 2 \log_{6} (7)$

Step 4

Rewrite $\log_{6} (8)$ as $\log_{6} (2^{3})$ .

$2 \log_{6} (2^{3}) + 2 \log_{6} (7)$

Step 5

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

$2 (3 \log_{6} (2)) + 2 \log_{6} (7)$

Step 6

Multiply $3$ by $2$ .

$6 \log_{6} (2) + 2 \log_{6} (7)$