Solve 7e^2x=1883

$$7 e ^ { 2 x } = 1883$$

Solve for x

$$x=\frac{\ln(269)}{2}\approx 2.79735569$$

Steps Using Definition of Logarithm

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

$$7e^{2x}=1883$$

Divide both sides by 7.

$$e^{2x}=269$$

Take the logarithm of both sides of the equation.

$$\log(e^{2x})=\log(269)$$

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

$$2x\log(e)=\log(269)$$

Divide both sides by \log(e).

$$2x=\frac{\log(269)}{\log(e)}$$

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

$$2x=\log_{e}\left(269\right)$$

Divide both sides by 2.

$$x=\frac{\ln(269)}{2}$$

Solve for x (complex solution)

$$x=\frac{\ln(269)}{2}+\pi n_{1}i$$

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