What is Log in Mathematics? 

In physics and math, logarithms are used for making calculations in easier manner. This is because they are the inverse of exponents and are used to solve problems that cannot be solved using only the exponent concept. 

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Originally, John Napier was the first person who introduced this concept to make calculations in an easy way and this concept quickly became popular among many scientists. He used logarithms to help with the multiplication of quantities like sines and also for finding the product of two numbers. He made use of the fact that the logarithms of the corresponding numbers could be found in a special table. This helped simplify long and tedious calculations. 

What is the difference between log and ln?

There are two kinds of logarithms: the common log (log10) and the natural log (ln). The latter is more commonly used in physics while the former is more common in mathematics. 

The common log is a base 10 log and ln is a base e log. The reason why l and n are reversed is lost to history but they can be found by studying the equation of a log and its base. 

What are the rules of logarithms?

There are a few rules that govern the writing of logs. One rule is that b, the base, stays as the base both in the exponent and log form. Another rule is that b doesn’t stay with x in the log form but instead, it stays with a. 

Whenever the bases of the logs are the same on both sides of an expression, then we can use a certain rule called the canceling rule to make the result more simple. This is similar to the product and quotient rules of exponents in that it requires b to be the base on both sides.