Solve e^x-1-a=0

$$e ^ { x } - 1 - a = 0$$

Solve for a

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

Steps for Solving Linear Equation

Subtract e^{x} from both sides. Anything subtracted from zero gives its negation.

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

Add 1 to both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -e^{x}+1 by -1.

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

Solve for x (complex solution)

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

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

$$a\neq -1$$

Solve for x

$$x=\ln(a+1)$$

$$a>-1$$