Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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