Precalculus Examples

$\log (a) + 3 \log (b) - \log (c)$

Step 1

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

$3 \log (b) + \log (\frac{a}{c})$

Step 2

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

$\log (b^{3}) + \log (\frac{a}{c})$

Step 3

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

$\log (b^{3} \frac{a}{c})$

Step 4

Combine $b^{3}$ and $\frac{a}{c}$ .

$\log (\frac{b^{3} a}{c})$