Start with: b^{x } = y.
b = base x = exponent y = power
If the base and exponent are given we compute a power. If the exponent and power are given we compute a root (or radical). If the power and base are given, we compute a
logarithm.
The logarithm of a number y with respect to a base b is the exponent to which b must be raised to obtain y.
b^{x} = y or x = log _{b }y
Examples:
10^{2} = 100 2 = log_{10 }100 10^{2} = 0.01 2 = log_{10} 0.01 10^{0} = 1 0 = log_{10} 1
2^{3} = 8 3 = log_{2} 8 3^{2} = 9 2 = log_{3} 9 25^{.5} = 5 .5 = log_{25} 5 2^{.5} = 1.414… .5 = log_{2} 1.414…
The most important logarithms in photography are those of base b = 2.
Logarithms of base b = 10 are known as common logarithms.
Logarithms of base e = 2.71828… are known as natural logarithms. (E is the base of the natural logarithm function, derived from the series 2 + ½ + 1/3 + ¼ + 1/5 …)
