Expand the Logarithmic Expression log base 3 of 8^3*9^8

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

Step 1

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

$\log_{3} (8^{3}) + \log_{3} (9^{8})$

Step 2

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

$3 \log_{3} (8) + \log_{3} (9^{8})$

Step 3

Expand $\log_{3} (9^{8})$ by moving $8$ outside the logarithm.

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

Step 4

Logarithm base $3$ of $9$ is $2$ .

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

Step 5

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

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

Step 6

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

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

Step 7

Multiply $3$ by $3$ .

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

Step 8

Multiply $8$ by $2$ .

$9 \log_{3} (2) + 16$