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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.


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