Algebra Examples

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

Step 1

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

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

Step 2

Simplify $- 3 \log_{2} (z)$ by moving $3$ inside the logarithm.

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

Step 3

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

$\log_{2} (\frac{\frac{x}{y}}{z^{3}})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Combine.

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

Step 6

Multiply $x$ by $1$ .

$\log_{2} (\frac{x}{y z^{3}})$