Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Move $x$ .

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

Step 3.2

Multiply $x$ by $x$ .

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

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

$\log (x^{2})$