Simplify/Condense 5 log base b of m- log base b of n

$5 \log_{b} (m) - \log_{b} (n)$

Step 1

Simplify $5 \log_{b} (m)$ by moving $5$ inside the logarithm.

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

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

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