Solve e^2x=17

$$e ^ { 2 x } = 17$$

Solve for x

$$x=\frac{\ln(17)}{2}\approx 1.416606672$$

Steps Using Definition of Logarithm

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

$$e^{2x}=17$$

Take the logarithm of both sides of the equation.

$$\log(e^{2x})=\log(17)$$

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

$$2x\log(e)=\log(17)$$

Divide both sides by \log(e).

$$2x=\frac{\log(17)}{\log(e)}$$

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

$$2x=\log_{e}\left(17\right)$$

Divide both sides by 2.

$$x=\frac{\ln(17)}{2}$$

Solve for x (complex solution)

$$x=\frac{\ln(17)}{2}+i\pi n_{1}$$

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