Expand the Logarithmic Expression log base 20 of m/(n^5p)

$\log_{20} (\frac{m}{n^{5} p})$

Step 1

Rewrite $\log_{20} (\frac{m}{n^{5} p})$ as $\log_{20} (m) - \log_{20} (n^{5} p)$ .

$\log_{20} (m) - \log_{20} (n^{5} p)$

Step 2

Rewrite $\log_{20} (n^{5} p)$ as $\log_{20} (n^{5}) + \log_{20} (p)$ .

$\log_{20} (m) - (\log_{20} (n^{5}) + \log_{20} (p))$

Step 3

Expand $\log_{20} (n^{5})$ by moving $5$ outside the logarithm.

$\log_{20} (m) - (5 \log_{20} (n) + \log_{20} (p))$

Step 4

Simplify each term.

Apply the distributive property.

$\log_{20} (m) - (5 \log_{20} (n)) - \log_{20} (p)$

Multiply $5$ by $- 1$ .

$\log_{20} (m) - 5 \log_{20} (n) - \log_{20} (p)$