A logarithm is an exponent. The logarithm (to the base 10) of 100 is 2 because 10² = 100. This can be abbreviated log₁₀100 = 2.

Because logarithms are exponents, they have an intimate connection with exponential functions and with the laws of exponents.

The basic relationship is b^x = y if and only if x = log_b y. Since 2³ = 8, log₂ 8 = 3. Since, according to a table of logarithms, log₁₀ 2 = .301, 10^.301 = 2.

The major laws of logarithms and the exponential laws from which they are derived are as follows:

I. log_b (xy) = log_b x + log_b y | bⁿ · b^m = b^n+m

II. log_b (x/y) = log_b x - log_b y | bⁿ/b^m = b^n-m

III. log_b x^y = y · log_b x | (bⁿ)^m = b^(nm)

IV. log_b x = (log_b a)(log_b x) | If x = b^r; b = a^p, then x...