Precalculus Examples

$\log_{3} (8) \cdot \log_{8} (9)$

Step 1

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

$\log_{3} (2^{3}) \cdot \log_{8} (9)$

Step 2

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

$3 \log_{3} (2) \cdot \log_{8} (9)$

Step 3

Rewrite $\log_{8} (9)$ as $\log_{8} (3^{2})$ .

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

Step 4

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

$3 \log_{3} (2) \cdot (2 \log_{8} (3))$

Step 5

Multiply $2$ by $3$ .

$6 \log_{3} (2) \log_{8} (3)$