Algebra Examples

${(x + 1)}^{{(x + 1)}^{3}} = 3$

Step 1

Simplify ${(x + 1)}^{{(x + 1)}^{3}}$ .

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Step 1.1

Use the Binomial Theorem.

${(x + 1)}^{x^{3} + 3 x^{2} \cdot 1 + 3 x \cdot 1^{2} + 1^{3}} = 3$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $3$ by $1$ .

${(x + 1)}^{x^{3} + 3 x^{2} + 3 x \cdot 1^{2} + 1^{3}} = 3$

Step 1.2.2

One to any power is one.

${(x + 1)}^{x^{3} + 3 x^{2} + 3 x \cdot 1 + 1^{3}} = 3$

Step 1.2.3

Multiply $3$ by $1$ .

${(x + 1)}^{x^{3} + 3 x^{2} + 3 x + 1^{3}} = 3$

Step 1.2.4

One to any power is one.

${(x + 1)}^{x^{3} + 3 x^{2} + 3 x + 1} = 3$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 0.44224957$

Step 3