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Published online by Cambridge University Press: 05 July 2011
220. Resuming the equation ab = c, we shall begin by remarking that, in the doctrine of Logarithms, we assume for the root a, a certain number taken at pleasure, and suppose this root to preserve invariably its assumed value. This being laid down, we take the exponent b such, that the power ab becomes equal to a given number c; in which case this exponent b is said to be the logarithm of the number c. To express this, we shall use the letter L. or the initial letters log. Thus, by b = L. c, or b = log. c, we mean that b is equal to the logarithm of the number c, or that the logarithm of c is b.
221. We see then, that the value of the root a being once established, the logarithm of any number, c, is nothing more than the exponent of that power of a, which is equal to c: so that c being = ab, b is the logarithm of the power ab. If, for the present, we suppose b = 1, we have 1 for the logarithm of a1, and consequently log. a = 1; but if we suppose b = 2, we have 2 for the logarithm of a2; that is to say, log. a2 = 2, and we may, in the same manner, obtain log. a3 = 3; log. a4 = 4; log. a5 = 5, and so on.
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