Precalculus Examples

$\log_{4} (6^{3} \cdot 11^{3})$

Step 1

Rewrite $\log_{4} (6^{3} \cdot 11^{3})$ as $\log_{4} (6^{3}) + \log_{4} (11^{3})$ .

$\log_{4} (6^{3}) + \log_{4} (11^{3})$

Step 2

Expand $\log_{4} (6^{3})$ by moving $3$ outside the logarithm.

$3 \log_{4} (6) + \log_{4} (11^{3})$

Step 3

Expand $\log_{4} (11^{3})$ by moving $3$ outside the logarithm.

$3 \log_{4} (6) + 3 \log_{4} (11)$

Step 4

Rewrite $\log_{4} (6)$ as $\log_{4} (2 (3))$ .

$3 \log_{4} (2 (3)) + 3 \log_{4} (11)$

Step 5

Rewrite $\log_{4} (2 (3))$ as $\log_{4} (2) + \log_{4} (3)$ .

$3 (\log_{4} (2) + \log_{4} (3)) + 3 \log_{4} (11)$

Step 6

Logarithm base $4$ of $2$ is $\frac{1}{2}$ .

$3 (\frac{1}{2} + \log_{4} (3)) + 3 \log_{4} (11)$

Step 7

Apply the distributive property.

$3 (\frac{1}{2}) + 3 \log_{4} (3) + 3 \log_{4} (11)$

Step 8

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} + 3 \log_{4} (3) + 3 \log_{4} (11)$