Solve 2^x=a+2/a-1

$$2 ^ { x } = \frac { a + 2 } { a - 1 }$$

Solve for a

$$a=\frac{2^{x}+2}{2^{x}-1}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable a cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by a-1.

$$\left(a-1\right)\times 2^{x}=a+2$$

Use the distributive property to multiply a-1 by 2^{x}.

$$a\times 2^{x}-2^{x}=a+2$$

Subtract a from both sides.

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

Add 2^{x} to both sides.

$$a\times 2^{x}-a=2+2^{x}$$

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 2^{x}-1.

$$\frac{\left(2^{x}-1\right)a}{2^{x}-1}=\frac{2^{x}+2}{2^{x}-1}$$

Dividing by 2^{x}-1 undoes the multiplication by 2^{x}-1.

$$a=\frac{2^{x}+2}{2^{x}-1}$$

Variable a cannot be equal to 1.

$$a=\frac{2^{x}+2}{2^{x}-1}\text{, }a\neq 1$$