Precalculus Examples

$\log_{5} (\frac{25 m^{4}}{n^{5}})$

Step 1

Rewrite $\log_{5} (\frac{25 m^{4}}{n^{5}})$ as $\log_{5} (25 m^{4}) - \log_{5} (n^{5})$ .

$\log_{5} (25 m^{4}) - \log_{5} (n^{5})$

Step 2

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

$\log_{5} (25 m^{4}) - (5 \log_{5} (n))$

Step 3

Multiply $5$ by $- 1$ .

$\log_{5} (25 m^{4}) - 5 \log_{5} (n)$

Step 4

Rewrite $\log_{5} (25 m^{4})$ as $\log_{5} (25) + \log_{5} (m^{4})$ .

$\log_{5} (25) + \log_{5} (m^{4}) - 5 \log_{5} (n)$

Step 5

Expand $\log_{5} (m^{4})$ by moving $4$ outside the logarithm.

$\log_{5} (25) + 4 \log_{5} (m) - 5 \log_{5} (n)$

Step 6

Logarithm base $5$ of $25$ is $2$ .

$2 + 4 \log_{5} (m) - 5 \log_{5} (n)$