Common and Natural Logarithms:

In  scientific  and  engineering  practice,  a  natural  system  of  logarithms  uses  the  number 2.718281828459042. Because this number is often encountered, the letter e is used.  Several natural occurrences can be expressed by exponential equations along with e as the base. For instance, the decay of radioactive isotopes can be expressed as a natural logarithm equation. These logarithmic expressions are known as natural logs because e is the basis for several laws of nature.

The expression ln is used to represent a logarithm when e is the base.  thus, the exponential equation is written as

e^x  = N.

and the logarithm expression is written as given below

log_e  N = x   or   lnN = x.

Since with base 10 logs (common logs), natural logs can be determined easily with the aid of a calculator.

Base 10 logs are often referred to as common logs. Since base 10 is the most hugely used number base, the "10" from the designation log₁₀ is frequent dropped. Therefore, any time "log" is used without a base specified, one should suppose that base 10 is being used.