# 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 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).