Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Combine $\frac{x^{3}}{y}$ and $z$ .

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