Number `e`. Function `y=e^x`. Function `y=ln(x)`

Among exponential function `y=a^x`, where a>1, special interest for math and its applications is function that has following property: tangent line to the graph of the function at point (0;1) forms with x-axis `45^0` angle (see left figure). Base a of such function `y=a^x` is denoted by letter e, i.e. `y=e^x`. It is calculated that exponent and natural logarithm`e=2.718281824590...`. e is irrational number and can be represented as following sum: `e=1+1/1+1/(1*2)+1/(1*2*3)+...+1/(1*2*3*...*n)+...`.

Using this equality we can find e with any precision.

Function `y=e^x` is called exponent.

Logarithmic function, that is inverse to exponent `y=e^x`, i.e. function `y=log_e(x)`, is denoted by `y=ln(x)` (where ln is read as "natural logarithm").

Graphs of functions `y=e^x` and `y=ln(x)` are symmetric about line y=x (see right figure).