The exponential function

The relationship between three numbers represented as a, b  and c:   

a =b^c

forms the basis of the definition of a logarithm: 

c  = log_b a

Logarithms can be defined to any base b, but commonly to base 10. The second important value that base b can take is the exponential number (also known as Euler's number) which approximates to 2.718, and which is denoted by the symbol e. The exponential of a variable x is then written as e^x, or exp(x) which is particularly useful when x  is replaced by a more complicated expression. (Note: textbooks traditionally introduced the exponential function as a power series,¹ but more recently this approach has remained the province of more advanced textbooks.)