Write as a Single Logarithm log base b of 8-2 log base b of 2

$\log_{b} (8) - 2 \log_{b} (2)$

Step 1

Simplify each term.

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

$\log_{b} (8) - \log_{b} (2^{2})$

Raise $2$ to the power of $2$ .

$\log_{b} (8) - \log_{b} (4)$

Step 2

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

$\log_{b} (\frac{8}{4})$

Step 3

Divide $8$ by $4$ .

$\log_{b} (2)$