Solve x[n]=alpha^n

$$x [ n ] = \alpha ^ { n }$$

Solve for x (complex solution)

$$x=\frac{\alpha ^{n}}{n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$nx=\alpha ^{n}$$

Divide both sides by n.

$$\frac{nx}{n}=\frac{\alpha ^{n}}{n}$$

Dividing by n undoes the multiplication by n.

$$x=\frac{\alpha ^{n}}{n}$$

Solve for x

$$x=\frac{\alpha ^{n}}{n}$$

$$\left(n\neq 0\text{ and }\alpha >0\right)\text{ or }\left(\alpha =0\text{ and }n>0\right)\text{ or }\left(n\neq 0\text{ and }\alpha <0\text{ and }Denominator(n)\text{bmod}2=1\right)$$

Steps for Solving Linear Equation

The equation is in standard form.

$$nx=\alpha ^{n}$$

Divide both sides by n.

$$\frac{nx}{n}=\frac{\alpha ^{n}}{n}$$

Dividing by n undoes the multiplication by n.

$$x=\frac{\alpha ^{n}}{n}$$