A logarithmic expression involves at least three quantities: the base, the exponent and the argument. In the expression log10(1) = 0, 10 is the base, 0 is the exponent, and 1 is the argument. Log10(1) is equal to 0, because 10 to the power of 0 is equal to 1. In general, the expression logA(b) = c means that A to the power of c is equal to b
In an equation involving multiple logarithmic expressions, the logarithms can be combined and simplified provided that they have the same base. When logarithms with base A are added, the sum can be simplified to the logarithm base A of the product of the exponents: logA(3) + logA(5) = logA(15). When logarithms with the same base are subtracted, the difference simplifies to the logarithm of the quotient of the exponents: logA(3) - logA(5) = logA(3/5). If the argument of a logarithm contains an exponent, the exponent can be re-written as a multiplier of the logarithm: logA(3^5) = 5*logA(3).
Logarithms with base 10 and e are pre-programmed into most calculators. To convert LogA(x) to base B, use the formula logB(x)/logB(a). This quotient has the same numerical value as logA(x) and, for B = 10 or B = e, is simpler to calculate.