Precalculus Examples

$2 \log_{2} (x) + \log_{2} (12) - \log_{2} (y)$

Step 1

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

$2 \log_{2} (x) + \log_{2} (\frac{12}{y})$

Step 2

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

$\log_{2} (x^{2}) + \log_{2} (\frac{12}{y})$

Step 3

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

$\log_{2} (x^{2} \frac{12}{y})$

Step 4

Combine $x^{2}$ and $\frac{12}{y}$ .

$\log_{2} (\frac{x^{2} \cdot 12}{y})$

Step 5

Move $12$ to the left of $x^{2}$ .

$\log_{2} (\frac{12 x^{2}}{y})$