Solve e^-y=0.756

$$e ^ { - y } = 0.756$$

Solve for y

$$y=\ln(\frac{250}{189})\approx 0.279713903$$

Steps Using Definition of Logarithm

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

$$e^{-y}=0.756$$

Take the logarithm of both sides of the equation.

$$\log(e^{-y})=\log(0.756)$$

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

$$-y\log(e)=\log(0.756)$$

Divide both sides by \log(e).

$$-y=\frac{\log(0.756)}{\log(e)}$$

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

$$-y=\log_{e}\left(0.756\right)$$

Divide both sides by -1.

$$y=\frac{\ln(\frac{189}{250})}{-1}$$

Solve for y (complex solution)

$$y=-i\times 2\pi n_{1}+\ln(\frac{250}{189})$$

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