Solve e^4x=120

$$e ^ { 4 x } = 120$$

Solve for x

$$x=\frac{\ln(120)}{4}\approx 1.196872936$$

Steps Using Definition of Logarithm

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

$$e^{4x}=120$$

Take the logarithm of both sides of the equation.

$$\log(e^{4x})=\log(120)$$

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

$$4x\log(e)=\log(120)$$

Divide both sides by \log(e).

$$4x=\frac{\log(120)}{\log(e)}$$

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

$$4x=\log_{e}\left(120\right)$$

Divide both sides by 4.

$$x=\frac{\ln(120)}{4}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{2}+\frac{\ln(120)}{4}$$

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