Solve e^2y=4

$$e ^ { 2 y } = 4$$

Solve for y

$$y=\ln(2)\approx 0.693147181$$

Steps Using Definition of Logarithm

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

$$e^{2y}=4$$

Take the logarithm of both sides of the equation.

$$\log(e^{2y})=\log(4)$$

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

$$2y\log(e)=\log(4)$$

Divide both sides by \log(e).

$$2y=\frac{\log(4)}{\log(e)}$$

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

$$2y=\log_{e}\left(4\right)$$

Divide both sides by 2.

$$y=\frac{2\ln(2)}{2}$$