Precalculus Examples

$\ln (4 x^{2} - 4 x) + \ln (\frac{1}{4 x})$

Step 1

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

$\ln ((4 x^{2} - 4 x) \frac{1}{4 x})$

Step 2

Multiply $4 x^{2} - 4 x$ by $\frac{1}{4 x}$ .

$\ln (\frac{4 x^{2} - 4 x}{4 x})$

Step 3

Factor $4 x$ out of $4 x^{2} - 4 x$ .

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Step 3.1

Factor $4 x$ out of $4 x^{2}$ .

$\ln (\frac{4 x (x) - 4 x}{4 x})$

Step 3.2

Factor $4 x$ out of $- 4 x$ .

$\ln (\frac{4 x (x) + 4 x (- 1)}{4 x})$

Step 3.3

Factor $4 x$ out of $4 x (x) + 4 x (- 1)$ .

$\ln (\frac{4 x (x - 1)}{4 x})$

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Cancel the common factor.

$\ln (\frac{4 x (x - 1)}{4 x})$

Step 4.2

Rewrite the expression.

$\ln (\frac{x (x - 1)}{x})$

Step 5

Cancel the common factor of $x$ .

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Step 5.1

Cancel the common factor.

$\ln (\frac{x (x - 1)}{x})$

Step 5.2

Divide $x - 1$ by $1$ .

$\ln (x - 1)$