Solve 2e^x-2=0

$$2 { e }^{ x } -2=0$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$2e^{x}-2=0$$

Add 2 to both sides of the equation.

$$2e^{x}=2$$

Divide both sides by 2.

$$e^{x}=1$$

Take the logarithm of both sides of the equation.

$$\log(e^{x})=\log(1)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$x\log(e)=\log(1)$$

Divide both sides by \log(e).

$$x=\frac{\log(1)}{\log(e)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$x=\log_{e}\left(1\right)$$

Solve for x (complex solution)

$$x=2\pi n_{1}i$$

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