Solve 6.27=e^x

$$6.27 = e ^ { x }$$

Solve for x

$$x=\ln(6.27)\approx 1.835776355$$

Steps Using Definition of Logarithm

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

$$e^{x}=6.27$$

Take the logarithm of both sides of the equation.

$$\log(e^{x})=\log(6.27)$$

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

$$x\log(e)=\log(6.27)$$

Divide both sides by \log(e).

$$x=\frac{\log(6.27)}{\log(e)}$$

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

$$x=\log_{e}\left(6.27\right)$$

Solve for x (complex solution)

$$x=\ln(6.27)+i\times 2\pi n_{1}$$

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