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:

10² = 100         2 = log₁₀ 100
10^-2 = 0.01          -2 = log₁₀ 0.01
10⁰ = 1         0 = log₁₀ 1
2³ = 8         3 = log₂ 8
3² = 9         2 = log₃ 9
25^.5 = 5         .5 = log₂₅ 5
2^.5 = 1.414…          .5 = log₂ 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 …)

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