Solve 2e^x=9

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

Solve for x

$$x=-\ln(\frac{2}{9})\approx 1.504077397$$

Steps Using Definition of Logarithm

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

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

Divide both sides by 2.

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

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(e).

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

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

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

Solve for x (complex solution)

$$x=-\ln(\frac{2}{9})+2\pi n_{1}i$$

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