When Napier first introduced Logarithms back in the 1600s, he thought that this was a neat little way to do calculations and increase mathematical efficiency. It was not until Euler came along and introduced the two most frequently used forms of Logarithms: — 1) Natural and 2) Common.
When we talk about a logarithm to the base ‘e’, we call it the natural logarithm of that number. It is commonly represented as ln(x) for some positive number x¹.
When someone mentions a common Logarithm, it is the logarithm to the base of ‘10’. It is commonly represented as: