Use wikipedia for a formal definition.

Natural logarithm - Wikipedia, the free encyclopedia

Suppose you have e^(2x + 3) = e^(50x) and you wanted to solve for x;

In order to negate the e's, you would use ln;

ln(e^(2x + 3)) = ln(e^(50x))

2x + 3 = 5x

Further, ln(x) is an exponential function.

It crosses the x-axis at (1,0), (whereas e^(x) cross the y axis at (0,1).

There are are many uses for the natural log. Take a look at the wikipedia site and then list any questions you have thereafter.