Precalculus Examples

$\log_{2} (x) - \log_{2} (y - 1) - \log_{2} (z + 3)$

Step 1

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

$\log_{2} (\frac{x}{y - 1}) - \log_{2} (z + 3)$

Step 2

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

$\log_{2} (\frac{\frac{x}{y - 1}}{z + 3})$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\log_{2} (\frac{x}{y - 1} \cdot \frac{1}{z + 3})$

Step 4

Multiply $\frac{x}{y - 1}$ by $\frac{1}{z + 3}$ .

$\log_{2} (\frac{x}{(y - 1) (z + 3)})$