The logarithm of a positive real number x to the base-a is the number y that satisfies the equation a^y = x. In symbols, the logarithm of x to the base-a is log_a x, and, if a^y = x, then y = log_a x.

Essentially, the logarithm to base-a is a function: To each positive real number x, the logarithm to base-a assigns x a number y such that a^y = x. For example, 10² = 100; therefore, log₁₀ 100 = 2. The logarithm of 100 to base-10 is 2, which is an elaborate name for the power of 10 that equals 100.

Any positive real number except 1 can be used as the base. However, the two most useful integer bases are 10 and 2. Base-2, also known as the binary system, is used in computer science because nearly all computers and calculators use base-2 for their internal calculations. Logarithms to the base-10 are called...