Simplify/Condense log base b of 9-2 log base b of 3

$\log_{b} (9) - 2 \log_{b} (3)$

Step 1

Simplify each term.

Simplify $- 2 \log_{b} (3)$ by moving $2$ inside the logarithm.

$\log_{b} (9) - \log_{b} (3^{2})$

Raise $3$ to the power of $2$ .

$\log_{b} (9) - \log_{b} (9)$

Step 2

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

$\log_{b} (\frac{9}{9})$

Step 3

Divide $9$ by $9$ .

$\log_{b} (1)$

Step 4

Logarithm base $b$ of $1$ is $0$ .

$0$