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 log2(x) + log2(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 log2. 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 logax = y is the same as ay = 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 logax = 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 x2 or a7.
- Logarithmic calculation: logax = y
- Exponential calculation: ay = 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 log2(x) = 4
The question is telling you that a log (on the left side) equals a number (on the right side), so:
24 = x
16 = x