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## Difference Between log and Natural log

log vs Natural log

In simple terms, logs are exponents and can take any positive value as their base. Logarithms are very useful mathematical concepts that have simplified complex mathematical calculations. Out of n number of bases, there are two values that for historical reasons are considered to be more useful than other values. Log with base 10, or common log as it is popularly known is written as log x. This common log is used in most of exponential scales in chemistry such as pH scale (for measurement of acidity and alkalinity), Richter scale (for measurement of intensity of earthquakes), and so on. It is so common that if you find no base written, you can assume it to be log x or common log.

However, there is another value of base that is very popular and is known as natural log. This article explains the difference between log and natural log to make it easier for budding mathematicians.

Natural log, or base e log, or simply ln x (pronounced ell-enn of x) is a logarithm to the base e, which is an irrational constant and whose value is taken as 2.718281828. Natural log of a number is the power to which e has to be raised to be equal to the number. We know that e X e = 7.389, hence ln (7.389) = 2.

On the other hand, 10 X 10 = 100

Hence, log 100 = 2

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