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Base
A base is used in power functions, exponential functions, logarithmic functions and in numeral systems.
Example 1
In a power function, the variable base x is raised to the fixed exponent n
f (x) = xn
Example 2
In an exponential function, the fixed base a is raised to the variable exponent x
f (x) = ax
Example 3
In a logarithmic function, you have a fixed base a and a variable x
f (x) = loga x
For a natural logarithm you use the base e, what you indicate by ln x or loge x.
Example 4
In a positional numeral system, the base is the number of unique numerals, including zero, for a position. By decimal numbers you have base 10.