Precalculus Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$3 \log (a B) - \log (c) - 2$

Step 1.2

Simplify $3 \log (a B)$ by moving $3$ inside the logarithm.

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

Step 1.3

Apply the product rule to $a B$ .

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

Step 2

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

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