Solve 6*e^y=200

$$6 \cdot e ^ { y } = 200$$

Solve for y

$$y=-\ln(\frac{3}{100})\approx 3.506557897$$

Steps Using Definition of Logarithm

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

$$6e^{y}=200$$

Divide both sides by 6.

$$e^{y}=\frac{100}{3}$$

Take the logarithm of both sides of the equation.

$$\log(e^{y})=\log(\frac{100}{3})$$

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

$$y\log(e)=\log(\frac{100}{3})$$

Divide both sides by \log(e).

$$y=\frac{\log(\frac{100}{3})}{\log(e)}$$

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

$$y=\log_{e}\left(\frac{100}{3}\right)$$

Solve for y (complex solution)

$$y=-\ln(\frac{3}{100})+2\pi n_{1}i$$

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