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Mathematics in Business and Economics
Logs
A logarithm is a particular form of power. A log is the power that a number must be raised to to get another number. This will all depend on the base that we are working in. If we are working in base 10 then the log of 10,000 would be 4 because 104 = 10,000. If we were working in base 5 then the log of 625 would be 4 because 54 = 625. With logs, therefore, you have to ask yourself the question, what is the number to which X must be raised to get the desired number?
Roots
If you understand powers and logs, it is a short step to understanding roots. If 2² is 4 then the square root of 4 is 2. The root of a number, therefore, is the value which when raised to a particular power gives you the original number. We can also make use of negative powers here as well. The cubed root of 27 is 3 because the value which you have to raise 3 to get 27 is 3 (3³ = 27). But 27 raised to the power of -3 is the same as 1⁄273. This begins to incorporate a number of the rules we covered in dealing with powers.
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