Precalculus Examples

$2 (2 \ln (x) - \ln (x + x) - \ln (x - 1))$

Step 1

Add $x$ and $x$ .

$2 (2 \ln (x) - \ln (2 x) - \ln (x - 1))$

Step 2

Rewrite $\ln (2 x)$ as $\ln (2) + \ln (x)$ .

$2 (2 \ln (x) - (\ln (2) + \ln (x)) - \ln (x - 1))$

Step 3

Apply the distributive property.

$2 (2 \ln (x) - \ln (2) - \ln (x) - \ln (x - 1))$

Step 4

Subtract $\ln (x)$ from $2 \ln (x)$ .

$2 (\ln (x) - \ln (2) - \ln (x - 1))$

Step 5

Apply the distributive property.

$2 \ln (x) + 2 (- \ln (2)) + 2 (- \ln (x - 1))$

Step 6

Simplify.

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Step 6.1

Multiply $- 1$ by $2$ .

$2 \ln (x) - 2 \ln (2) + 2 (- \ln (x - 1))$

Step 6.2

Multiply $- 1$ by $2$ .

$2 \ln (x) - 2 \ln (2) - 2 \ln (x - 1)$