Question 133333
We can get a solution by changing the exponential equation to log form.

Take natural log of both sides of the equation.

In(e^x) = In(2)

The left side becomes x because the natural log of e^x is just x.

We now have this:

x = In(2)

Use calculator to find x.

x = 0.693

NOTE:  I also want to add that the decimal number 0.6931471806 can be rounded off to three decimal places.  This is why I selected the approximate value for x = 0.693

Is this clear?