Solve 2^x=2(a+1)

$$2 ^ { x } = 2 ( a + 1 )$$

Solve for a

$$a=\frac{2^{x}-2}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by a+1.

$$2^{x}=2a+2$$

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

$$2a+2=2^{x}$$

Subtract 2 from both sides.

$$2a=2^{x}-2$$

Divide both sides by 2.

$$\frac{2a}{2}=\frac{2^{x}-2}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{2^{x}-2}{2}$$

Divide 2^{x}-2 by 2.

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

Solve for x (complex solution)

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

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

$$a\neq -1$$

Solve for x

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

$$a>-1$$