Precalculus Examples

$\log (a) + 2 \log (B) - 3 \log (C)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log (B)$ by moving $2$ inside the logarithm.

$\log (a) + \log (B^{2}) - 3 \log (C)$

Step 1.2

Simplify $- 3 \log (C)$ by moving $3$ inside the logarithm.

$\log (a) + \log (B^{2}) - \log (C^{3})$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (a B^{2}) - \log (C^{3})$

Step 3

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

$\log (\frac{a B^{2}}{C^{3}})$