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Base
a is the base of the exponential expression ax. a is also the base of the logarithmic expression logax.
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Common Logarithmic Function
The logarithmic function f (x) = log10x.
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Exponent
x is the exponent in the exponential expression ax. It means a is multiplied by itself x times.
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Exponential Function
A function of the form f (x) = ax, where a > 0, a≠1, and x is any real number
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Half-life
The time it takes for a exponentially decaying substance to lose half its mass.
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Logarithm
An expression of the form logax. If logax = b, ab = x.
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Logarithmic Function
A function of the form y = logax where x = ay, a > 0, and a≠1. This example is a logarithmic function with base a.
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Natural Exponential Function
The function f (x) = ex.
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Natural Logarithmic Function
The logarithmic function f (x) = logex = ln x.
Terms
Formulae
Change of Base | logax = , where a, b, and x are all positive real numbers and a, b≠1. |