Common & Natural Logarithms

In this section, we continue to learn about logarithms. In our previous dealings with logarithms, we treated a logarithm with a base of 10 as any other logarithm. When we encounter a base 10 logarithm, it is referred to as a common logarithm. The common logarithm does not require us to list the base of 10. If we see log(x), this is telling us we have log base 10 of x. Another important logarithm is known as the natural logarithm. The natural logarithm has a base of e. The value for e is given as an approximation. Just like with pi, e is an irrational number. This means the decimal form of the number will not terminate nor repeat the same pattern. Lastly, we will discuss the change of base rule. This rule allows us to change the base of a logarithm into one that is more convenient to work with. The most practical use of this formula is to convert a logarithm to a common logarithm or a natural logarithm. This would allow us to approximate the answer quickly using most calculators.