Solve 5e^x+2=8

$$5 e ^ { x } + 2 = 8$$

Solve for x

$$x=\ln(\frac{6}{5})\approx 0.182321557$$

Steps Using Definition of Logarithm

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

$$5e^{x}+2=8$$

Subtract 2 from both sides of the equation.

$$5e^{x}=6$$

Divide both sides by 5.

$$e^{x}=\frac{6}{5}$$

Take the logarithm of both sides of the equation.

$$\log(e^{x})=\log(\frac{6}{5})$$

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

$$x\log(e)=\log(\frac{6}{5})$$

Divide both sides by \log(e).

$$x=\frac{\log(\frac{6}{5})}{\log(e)}$$

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

$$x=\log_{e}\left(\frac{6}{5}\right)$$

Solve for x (complex solution)

$$x=\ln(\frac{6}{5})+2\pi n_{1}i$$

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