Solve lim(1+e^x)^frac{1{x}}=e

$$\lim ( 1 + e ^ { x } ) ^ { \frac { 1 } { x } } = e$$

Solve for l

$$l=e\left(Im(e^{x})\right)^{-\frac{1}{x}}$$

$$\left(Im(e^{x})\right)^{\frac{1}{x}}\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\left(Im(e^{x})\right)^{\frac{1}{x}}l=e$$

Divide both sides by \left(Im(e^{x})\right)^{x^{-1}}.

$$\frac{\left(Im(e^{x})\right)^{\frac{1}{x}}l}{\left(Im(e^{x})\right)^{\frac{1}{x}}}=\frac{e}{\left(Im(e^{x})\right)^{\frac{1}{x}}}$$

Dividing by \left(Im(e^{x})\right)^{x^{-1}} undoes the multiplication by \left(Im(e^{x})\right)^{x^{-1}}.

$$l=\frac{e}{\left(Im(e^{x})\right)^{\frac{1}{x}}}$$

Divide e by \left(Im(e^{x})\right)^{x^{-1}}.

$$l=e\left(Im(e^{x})\right)^{-\frac{1}{x}}$$