Statistics Definitions > What are Logarithms?

## Logarithms in Statistics

Now and then you’ll come across a logarithm or two in stats, although they **aren’t widely used.** If you’ve worked with logarithms before (perhaps in algebra), you may remember having to rearrange logs and solve some pretty complex equations like log_{2}(x) + log_{2}(x-2) = 3. You probably won’t see these types of equations in elementary statistics, but you *might* see the occasional use of a log like log^{2}. All you really need to know about logarithms used in statistics is this simple fact:

What are Logarithms? Logarithms are simply an exponent in a different form. For example log

_{a}x = y is the same as a_{y}= x.

## Logarithms: Understanding in Steps

Let’s have a look at some of the steps that make logarithms easier to understand.

Step 1: **Understand the difference between logarithmic and exponential calculations: **

This is the first and probably the easiest step of all. If you find something like log_{a}x = y then it is a logarithmic problem. Always remember logarithmic problems are **always** denoted by letters “log”. If the calculation is in exponential format then the variable is denoted with a power, like x^{2} or a^{7}.

- Logarithmic calculation: log
_{a}x = y - Exponential calculation: a
^{y}= x

Step 2: **Understand various logarithmic parts:**

The *base *in logarithmic calculation is the *subscript* which you can find next to the letters *log *as shown in the example below. The base next to the word *log* is 3. The number following the subscript is known as the *argument *as shown in example which is number 10. Finally, the logarithmic expression is set equal to 4 in the example below.

**Sample problem:** Solve log_{2}(x) = 4

The question is telling you that a log (on the left side) equals a number (on the right side), so:

2^{4} = x

16 = x

i really love that explanation, i love them easy, I love them simple i will love to have more tips on the basis of log. thanks alot sir