Solve e^14x=402

$$e ^ { 14 x } = 402$$

Solve for x

$$x=\frac{\ln(402)}{14}\approx 0.428318006$$

Steps Using Definition of Logarithm

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

$$e^{14x}=402$$

Take the logarithm of both sides of the equation.

$$\log(e^{14x})=\log(402)$$

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

$$14x\log(e)=\log(402)$$

Divide both sides by \log(e).

$$14x=\frac{\log(402)}{\log(e)}$$

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

$$14x=\log_{e}\left(402\right)$$

Divide both sides by 14.

$$x=\frac{\ln(402)}{14}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{7}+\frac{\ln(402)}{14}$$

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