Simplify log of 2x+ log of x- log of 2

$\log (2 x) + \log (x) - \log (2)$

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

$\log (2 x \cdot x) - \log (2)$

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

$\log (\frac{2 x \cdot x}{2})$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\log (\frac{2 (x \cdot x)}{2})$

Multiply $x$ by $x$ .

$\log (\frac{2 x^{2}}{2})$

Cancel the common factor of $2$ .

Cancel the common factor.

$\log (\frac{2 x^{2}}{2})$

Divide $x^{2}$ by $1$ .

$\log (x^{2})$