Solve 2^x-m=2^x-1

$$2 ^ { x } - m = 2 ^ { x - 1 }$$

Solve for m

$$m=\frac{2^{x}}{2}$$

Steps for Solving Linear Equation

Subtract 2^{x} from both sides.

$$-m=2^{x-1}-2^{x}$$

Divide both sides by -1.

$$\frac{-m}{-1}=-\frac{\frac{2^{x}}{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$m=-\frac{\frac{2^{x}}{2}}{-1}$$

Divide -\frac{2^{x}}{2} by -1.

$$m=2^{x-1}$$

Solve for x (complex solution)

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

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

$$m\neq 0$$

Solve for x

$$x=\log_{2}\left(m\right)+1$$

$$m>0$$