Precalculus Examples

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

Step 1

Simplify $2 \ln (x - 1)$ by moving $2$ inside the logarithm.

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

Step 2

Exponentiation and log are inverse functions.

${(x - 1)}^{2}$

Step 3

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$(x - 1) (x - 1)$

Step 4

Expand $(x - 1) (x - 1)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$x (x - 1) - 1 (x - 1)$

Step 4.2

Apply the distributive property.

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

Step 4.3

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1$

$x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1$

Step 5.1.2

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1$

Step 5.1.3

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - 1 x - 1 \cdot - 1$

Step 5.1.4

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - x - 1 \cdot - 1$

Step 5.1.5

Multiply $- 1$ by $- 1$ .

$x^{2} - x - x + 1$

$x^{2} - x - x + 1$

Step 5.2

Subtract $x$ from $- x$ .

$x^{2} - 2 x + 1$

$x^{2} - 2 x + 1$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$