Difference between Log and Ln

In mathematics, logarithms and natural logarithms are widely used.

The main difference is that the logarithm is the power to which a given number must be raised to produce another number whereas the natural logarithm is the logarithm to the base e.

Before we move to the differences, let’s understand what are Log and Ln:

  • Log: A logarithm is an exponent that indicates how many times a base number must be multiplied by itself to obtain a given value. It is denoted as log.
  • Ln: A natural logarithm is a logarithm to the base e, where e is a mathematical constant approximately equal to 2.71828. It is denoted as ln.

Log vs Ln

Now, let’s move to Log vs Ln:

Major differences between Log and Ln

Log Ln
Logarithm has a base other than e. Natural logarithm has a base e.
Logarithm is a general term for a logarithmic function. Natural logarithm specifically refers to the logarithmic function with base e.
The inverse of a logarithmic function is an exponential function. The inverse of a natural logarithmic function is e raised to the power of the function.
Logarithm has various properties such as the power property, product property, and quotient property. Natural logarithm has only one property which is the power property.
Logarithm is widely used in engineering, science, and technology. Natural logarithm is widely used in calculus and mathematical analysis.


That’s it.

Note that sometimes, the question might also be asked as “distinguish between Log and Ln”.

Also see:

Final words

Logarithm and natural logarithm have some differences such as the base of the function, the properties, and the applications. Although they are similar, it is important to use the appropriate function depending on the context and the problem being solved.

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