Solve 5e^x+2=120

$$5 e ^ { x + 2 } = 120$$

Solve for x

$$x=\ln(24)-2\approx 1.17805383$$

Steps Using Definition of Logarithm

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

$$5e^{x+2}=120$$

Divide both sides by 5.

$$e^{x+2}=24$$

Take the logarithm of both sides of the equation.

$$\log(e^{x+2})=\log(24)$$

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

$$\left(x+2\right)\log(e)=\log(24)$$

Divide both sides by \log(e).

$$x+2=\frac{\log(24)}{\log(e)}$$

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

$$x+2=\log_{e}\left(24\right)$$

Subtract 2 from both sides of the equation.

$$x=\ln(24)-2$$

Solve for x (complex solution)

$$x=\ln(24)-2+2\pi n_{1}i$$

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