Precalculus Examples

$\ln (x) + \ln (1 - x)$

Step 1

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

$\ln (x (1 - x))$

Step 2

Apply the distributive property.

$\ln (x \cdot 1 + x (- x))$

Step 3

Simplify the expression.

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Step 3.1

Multiply $x$ by $1$ .

$\ln (x + x (- x))$

Step 3.2

Rewrite using the commutative property of multiplication.

$\ln (x - x \cdot x)$

Step 4

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

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Step 4.1

Move $x$ .

$\ln (x - (x \cdot x))$

Step 4.2

Multiply $x$ by $x$ .

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