Precalculus Examples

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

Step 1

Simplify $4 \ln (x - 2)$ by moving $4$ inside the logarithm.

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

Step 2

Exponentiation and log are inverse functions.

${(x - 2)}^{4}$

Step 3

Use the Binomial Theorem.

$x^{4} + 4 x^{3} \cdot - 2 + 6 x^{2} {(- 2)}^{2} + 4 x {(- 2)}^{3} + {(- 2)}^{4}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Multiply $- 2$ by $4$ .

$x^{4} - 8 x^{3} + 6 x^{2} {(- 2)}^{2} + 4 x {(- 2)}^{3} + {(- 2)}^{4}$

Step 4.2

Raise $- 2$ to the power of $2$ .

$x^{4} - 8 x^{3} + 6 x^{2} \cdot 4 + 4 x {(- 2)}^{3} + {(- 2)}^{4}$

Step 4.3

Multiply $4$ by $6$ .

$x^{4} - 8 x^{3} + 24 x^{2} + 4 x {(- 2)}^{3} + {(- 2)}^{4}$

Step 4.4

Raise $- 2$ to the power of $3$ .

$x^{4} - 8 x^{3} + 24 x^{2} + 4 x \cdot - 8 + {(- 2)}^{4}$

Step 4.5

Multiply $- 8$ by $4$ .

$x^{4} - 8 x^{3} + 24 x^{2} - 32 x + {(- 2)}^{4}$

Step 4.6

Raise $- 2$ to the power of $4$ .

$x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16$