Solve 5e^4n=95

$$5 e ^ { 4 n } = 95$$

Solve for n

$$n=\frac{\ln(19)}{4}\approx 0.736109745$$

Steps Using Definition of Logarithm

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

$$5e^{4n}=95$$

Divide both sides by 5.

$$e^{4n}=19$$

Take the logarithm of both sides of the equation.

$$\log(e^{4n})=\log(19)$$

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

$$4n\log(e)=\log(19)$$

Divide both sides by \log(e).

$$4n=\frac{\log(19)}{\log(e)}$$

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

$$4n=\log_{e}\left(19\right)$$

Divide both sides by 4.

$$n=\frac{\ln(19)}{4}$$

Solve for n (complex solution)

$$n=\frac{\pi n_{1}i}{2}+\frac{\ln(19)}{4}$$

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