Solve e^2x-9=0

$${ e }^{ 2x } -9=0$$

Solve for x

$$x=\ln(3)\approx 1.098612289$$

Steps Using Definition of Logarithm

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

$$e^{2x}-9=0$$

Add 9 to both sides of the equation.

$$e^{2x}=9$$

Take the logarithm of both sides of the equation.

$$\log(e^{2x})=\log(9)$$

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

$$2x\log(e)=\log(9)$$

Divide both sides by \log(e).

$$2x=\frac{\log(9)}{\log(e)}$$

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

$$2x=\log_{e}\left(9\right)$$

Divide both sides by 2.

$$x=\frac{2\ln(3)}{2}$$