Simplify/Condense 5 log base 2 of k-8 log base 2 of m+10 log base 2 of n

$5 \log_{2} (k) - 8 \log_{2} (m) + 10 \log_{2} (n)$

Step 1

Simplify each term.

Simplify $5 \log_{2} (k)$ by moving $5$ inside the logarithm.

$\log_{2} (k^{5}) - 8 \log_{2} (m) + 10 \log_{2} (n)$

Simplify $- 8 \log_{2} (m)$ by moving $8$ inside the logarithm.

$\log_{2} (k^{5}) - \log_{2} (m^{8}) + 10 \log_{2} (n)$

Simplify $10 \log_{2} (n)$ by moving $10$ inside the logarithm.

$\log_{2} (k^{5}) - \log_{2} (m^{8}) + \log_{2} (n^{10})$

Step 2

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

$\log_{2} (\frac{k^{5}}{m^{8}}) + \log_{2} (n^{10})$

Step 3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{2} (\frac{k^{5}}{m^{8}} n^{10})$

Step 4

Combine $\frac{k^{5}}{m^{8}}$ and $n^{10}$ .

$\log_{2} (\frac{k^{5} n^{10}}{m^{8}})$