(MATHEMATICS) a function of numbers that are the root of a base. For example, log(base 2) means a function of numbers that are the numbered roots of 2. The log(base 2) of 2 is 1, meaning 2 raised to the power of 1 is 2 (2^1 = 2); log(2) of 4 is 2, and so on.
The idea here is that any number can be expressed as 2 raised to some power; better still, if you do math with the logs of a number rather than the numbers themselves, you can find useful patterns. For example, if you are graphing population growth, and you just plot the raw number of people over time, you aren't going to notice anything in particular. If you plot the log of population, you can see that, while population is growing, the rate of growth is falling.
Usually, if you are doing statistical research with numbers that always have to be positive (like population, death tolls from diseases, etc.), you need to use logarithms for the numerical values in order to represent a confidence interval.
Logs usually have a base of e or 10. Logs with a base of e are called natural logs.
A logarithm is the inverse of an exponential function.
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