Precalculus Examples

$\log (x) + 2 \log (y) - \log (z)$

Step 1

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

$2 \log (y) + \log (\frac{x}{z})$

Step 2

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

$\log (y^{2}) + \log (\frac{x}{z})$

Step 3

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

$\log (y^{2} \frac{x}{z})$

Step 4

Combine $y^{2}$ and $\frac{x}{z}$ .

$\log (\frac{y^{2} x}{z})$