 # Difference Between Log and Ln

The difference between log and ln is important to understand, as logarithms by themselves are important concepts that need to be studied and analyzed. The log number is simply defined as the method of obtaining the number which has its power to a base of 10. A natural logarithm can simply be referred to as the power to which the base ‘e’ that has to be raised to obtain a number called as its log number. It was initially discovered in the 17th century by John Napier, who discovered and conceptualized the theory of logarithms.

## Key Differences Between Log and Ln

One must know the difference between log and ln, to solve logarithmic problems. Having a key understanding of the exponential function can also prove beneficial to understanding different concepts. Some of the key differences between the ln and log are given below:

Difference Between Log and Ln

Log

Ln

Log refers to a logarithm to the base 10

Ln refers to a logarithm to the base e

This is also called as a common logarithm

This is also called as a natural logarithm

The common log is represented as log10 (x)

The natural log is represented as loge (x)

The exponent form of the common logarithm is 10x =y

The exponent form of the natural logarithm is ex =y

The interrogative statement for the common logarithm is “At which number should we raise 10 to get y?” The interrogative statement for the natural logarithm is “At which number should we raise Euler’s constant number to get y?”
It is more widely used in physics when compared to ln

As logarithms are usually taken to the base in physics, ln is used much lesser

Mathematically, it is represented as log base 10 Mathematically, this is represented as log base e

Thus, this represents the key differences between log and ln. It is important to know these key differences.

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