Trigonometry Examples

$\log_{5} ({(m^{2} n^{3})}^{4})$

Step 1

Expand $\log_{5} ({(m^{2} n^{3})}^{4})$ by moving $4$ outside the logarithm.

$4 \log_{5} (m^{2} n^{3})$

Step 2

Rewrite $\log_{5} (m^{2} n^{3})$ as $\log_{5} (m^{2}) + \log_{5} (n^{3})$ .

$4 (\log_{5} (m^{2}) + \log_{5} (n^{3}))$

Step 3

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

$4 (2 \log_{5} (m) + \log_{5} (n^{3}))$

Step 4

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

$4 (2 \log_{5} (m) + 3 \log_{5} (n))$

Step 5

Apply the distributive property.

$4 (2 \log_{5} (m)) + 4 (3 \log_{5} (n))$

Step 6

Multiply $2$ by $4$ .

$8 \log_{5} (m) + 4 (3 \log_{5} (n))$

Step 7

Multiply $3$ by $4$ .

$8 \log_{5} (m) + 12 \log_{5} (n)$