Solve e^x+10=20

$$e ^ { x + 10 } = 20$$

Solve for x

$$x=\ln(20)-10\approx -7.004267726$$

Steps Using Definition of Logarithm

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

$$e^{x+10}=20$$

Take the logarithm of both sides of the equation.

$$\log(e^{x+10})=\log(20)$$

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

$$\left(x+10\right)\log(e)=\log(20)$$

Divide both sides by \log(e).

$$x+10=\frac{\log(20)}{\log(e)}$$

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

$$x+10=\log_{e}\left(20\right)$$

Subtract 10 from both sides of the equation.

$$x=\ln(20)-10$$

Solve for x (complex solution)

$$x=\ln(20)-10+2\pi n_{1}i$$

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