Precalculus Examples

$\log_{5} (7^{6} \cdot 8^{3})$

Step 1

Rewrite $\log_{5} (7^{6} \cdot 8^{3})$ as $\log_{5} (7^{6}) + \log_{5} (8^{3})$ .

$\log_{5} (7^{6}) + \log_{5} (8^{3})$

Step 2

Expand $\log_{5} (7^{6})$ by moving $6$ outside the logarithm.

$6 \log_{5} (7) + \log_{5} (8^{3})$

Step 3

Expand $\log_{5} (8^{3})$ by moving $3$ outside the logarithm.

$6 \log_{5} (7) + 3 \log_{5} (8)$

Step 4

Rewrite $\log_{5} (8)$ as $\log_{5} (2^{3})$ .

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

Step 5

Expand $\log_{5} (2^{3})$ by moving $3$ outside the logarithm.

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

Step 6

Multiply $3$ by $3$ .

$6 \log_{5} (7) + 9 \log_{5} (2)$