Solve 2^x-1=θ(pie)

$${ 2 }^{ x } -1= \theta ( \pi e)$$

Solve for θ

$$\theta =-\frac{1-2^{x}}{e\pi }$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\theta \pi e=2^{x}-1$$

The equation is in standard form.

$$e\pi \theta =2^{x}-1$$

Divide both sides by \pi e.

$$\frac{e\pi \theta }{e\pi }=\frac{2^{x}-1}{e\pi }$$

Dividing by \pi e undoes the multiplication by \pi e.

$$\theta =\frac{2^{x}-1}{e\pi }$$

Solve for x (complex solution)

$$x=\log_{2}\left(e\pi \theta +1\right)+\frac{2\pi n_{1}i}{\ln(2)}$$

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

$$\theta \neq -\frac{1}{e\pi }$$

Solve for x

$$x=\log_{2}\left(e\pi \theta +1\right)$$

$$\theta >-\frac{1}{e\pi }$$