Simplify/Condense log base 2 of xy- log base 2 of x^2

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

Step 1

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

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

Step 2

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $x y$ .

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

Cancel the common factors.

Factor $x$ out of $x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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