Algebra Examples

$3 \log_{b} (m) - 2 \log_{b} (n)$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

$\log_{b} (\frac{m^{3}}{n^{2}})$