Solve e^y=1

$$e ^ { y } = 1$$

Solve for y

$$y=0$$

Steps Using Definition of Logarithm

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

$$e^{y}=1$$

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(e).

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

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

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

Solve for y (complex solution)

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

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