tim- maybe you will shit some out
dan- ill get my calculator so we can logarithm afterwards.
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.
Logarithm is derived from Greek logos "reckoning, ratio," and arithmos "number."
10, -3,10^-3, 0.001 (or 1/1000) (line 1)
10, -2, 10^-2, 0.01 (or 1/100)
10, -1, 10^-1, 0.1 (or 1/10)
10, 0, 10^0, 1
10, 1, 10^1, 10
10, 2, 10^2, 100 (10 squared)
10, 3, 10^3, 1,000 (10 cubed)
And so forth.
Any positive real number can be expressed as the product of 10 raised to any real number; for example 100,000 can be written as 100 x 1000 = 10^2 x 10^3 = 10^5. Notice that the exponents are additive. It is easy to show that for division the exponents subtract.
Before the advent of hand-held electronic calculators, logarithms and the use of log tables reduced calculating time by converting long-hand multiplication into an addition process and long-hand division into a subtraction process where the result was accurate to three significant figures. One would just look up the logarithms of two or more numbers that were being multiplied, sum the logarithms, and then look up the corresponding number.
Another benefit of using logarithms is that curvilinear data points can be converted into linear data points, and the latter is easier to model with a first-order equation derived using either graph paper or linear regression analysis.