Precalculus Examples

$\log (\frac{6^{6}}{11^{36}})$

Step 1

Rewrite $\log (\frac{6^{6}}{11^{36}})$ as $\log (6^{6}) - \log (11^{36})$ .

$\log (6^{6}) - \log (11^{36})$

Step 2

Expand $\log (6^{6})$ by moving $6$ outside the logarithm.

$6 \log (6) - \log (11^{36})$

Step 3

Expand $\log (11^{36})$ by moving $36$ outside the logarithm.

$6 \log (6) - (36 \log (11))$

Step 4

Rewrite $\log (6)$ as $\log (2 (3))$ .

$6 \log (2 (3)) - (36 \log (11))$

Step 5

Rewrite $\log (2 (3))$ as $\log (2) + \log (3)$ .

$6 (\log (2) + \log (3)) - (36 \log (11))$

Step 6

Apply the distributive property.

$6 \log (2) + 6 \log (3) - (36 \log (11))$

Step 7

Multiply $36$ by $- 1$ .

$6 \log (2) + 6 \log (3) - 36 \log (11)$