A system of developing logarithms by considering a number as base is called system of logarithm.
Infinite number of logarithmic systems can be developed by considering infinite numbers as base but there are few logarithmic systems, which are really and widely in scientific applications in various fields. Here are three important logarithmic systems which play vital role in different fields of science.
John Napier introduced natural logarithmic system by using a mathematical concept $e$ to express any number into multiplicative factors of $e$.
Henry Briggs understood the complicity of Napier logarithm and introduced common logarithm by using $10$ as base to express any number into multiplicative terms of $10$.
Michael Stifel introduced Binary Logarithm by using $2$ as base to express any number into multiplicative terms of $2$.