Difference Between Log and ln

Log vs ln

Logarithm is a very useful mathematical concept that helps in solving complex math problems. Logarithms, simply speaking are exponents. The power to which a base of 10 must be raised to obtain a number is called its log number, and the power to which the base e must be raised to obtain a number is called the natural logarithm of the number. John Napier, a mathematician, introduced the concept of logarithms in the 17th century to make calculations easier. There are many who remain confused between log and ln, and this article tries to find out the differences between log and ln.

Log to the base 10 of 100 = 2, as 10X10= 100, that is Log10100 = Log10102 = 2

Here, 10 is the base, 2 is the logarithm, and 100 is the number whose log is 2. Logarithms to the base 10 are called common logarithms, or simply log. On the other hand, logarithms to the base e (loge) are called natural logarithms or simply ln (pronounced lon).

As for the difference between log and ln, and how they are related, take a look at the following equations.

Log x is the exponent of 10 that gives you a certain number. We know that 10X10=100, so log 100= 2

In a similar manner, ln x is an exponent of e and not 10, thus, giving a different result.

We know that e= 2.18281828459, and e X e = 7.389056

Hence ln 7.389056 = 2