Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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 $0$ .

$0$