Logarithms, LAWG uh rihth uhmz or LOG uh rihth uhmz, are numbers that are known in algebra as exponents. Exponents are used to express repeated multiplications of a single number. For example, 2 X 2 X 2 can be written 23. In the equation 23 = 8, 3 is the exponent and 2 is the base. Stated in terms of logarithms, 3 is the logarithm of the number 8 to the base 2. This statement can be written as log28 = 3. The equation log28 = 3 is another way of expressing 23 = 8. In general, if bx = p, then x = logbp.
Suppose you want to calculate the number of ancestors you have in each of three previous generations. You have 2 parents, so you have 2 ancestors in the first generation. This calculation can be expressed as 21 = 2. Each of your parents has 2 parents, so you have 2 X 2 = 22 = 4 ancestors in the second generation. Each of your grandparents has 2 parents, so you have 4 X 2 = 2 X 2 X 2 = 23 = 8 ancestors in the third generation. The calculation continues in this pattern. In which generation do you have 1,024 ancestors? That is, for which exponent x is it true that 2x = 1,024? You can find the answer by multiplying 2 by itself until you reach 1,024. But if you know that log21,024 = 10, you know the answer is 10.
