Solve e^x=1/a

$$e ^ { x } = \frac { 1 } { a }$$

Solve for a

$$a=\frac{1}{e^{x}}$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$ae^{x}=1$$

The equation is in standard form.

$$e^{x}a=1$$

Divide both sides by e^{x}.

$$\frac{e^{x}a}{e^{x}}=\frac{1}{e^{x}}$$

Dividing by e^{x} undoes the multiplication by e^{x}.

$$a=\frac{1}{e^{x}}$$

Variable a cannot be equal to 0.

$$a=\frac{1}{e^{x}}\text{, }a\neq 0$$

Solve for x (complex solution)

$$x=-\ln(a)+2\pi n_{1}i$$

$$n_{1}\in \mathrm{Z}$$

$$a\neq 0$$

Solve for x

$$x=-\ln(a)$$

$$a>0$$