Solve 13990={(e)^x}+3x

$$13990= {(e)^{ x }} +3x$$

Solve for x

$$x=\ln(13990)\approx 9.546098068$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$e^{x}=13990$$

Take the logarithm of both sides of the equation.

$$\log(e^{x})=\log(13990)$$

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

$$x\log(e)=\log(13990)$$

Divide both sides by \log(e).

$$x=\frac{\log(13990)}{\log(e)}$$

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

$$x=\log_{e}\left(13990\right)$$

Solve for x (complex solution)

$$x=\ln(13990)+2\pi n_{1}i$$

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