Precalculus Examples

$\log_{7} (10 \cdot 3 \cdot 11^{6})$

Step 1

Rewrite $\log_{7} (10 \cdot 3 \cdot 11^{6})$ as $\log_{7} (10 \cdot 3) + \log_{7} (11^{6})$ .

$\log_{7} (10 \cdot 3) + \log_{7} (11^{6})$

Step 2

Rewrite $\log_{7} (10 \cdot 3)$ as $\log_{7} (10) + \log_{7} (3)$ .

$\log_{7} (10) + \log_{7} (3) + \log_{7} (11^{6})$

Step 3

Expand $\log_{7} (11^{6})$ by moving $6$ outside the logarithm.

$\log_{7} (10) + \log_{7} (3) + 6 \log_{7} (11)$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Rewrite $\log_{7} (10)$ as $\log_{7} (2 (5))$ .

$\log_{7} (2 (5)) + \log_{7} (3) + 6 \log_{7} (11)$

Step 4.2

Rewrite $\log_{7} (2 (5))$ as $\log_{7} (2) + \log_{7} (5)$ .

$\log_{7} (2) + \log_{7} (5) + \log_{7} (3) + 6 \log_{7} (11)$