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