Precalculus Examples

$\log_{b} (4) - 2 \log_{b} (3 x)$

Step 1

Simplify each term.

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

$\log_{b} (4) - \log_{b} ({(3 x)}^{2})$

Apply the product rule to $3 x$ .

$\log_{b} (4) - \log_{b} (3^{2} x^{2})$

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

$\log_{b} (4) - \log_{b} (9 x^{2})$

Step 2

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

$\log_{b} (\frac{4}{9 x^{2}})$