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natural logarithm


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The natural logarithm of a positive real number a is denoted by lna and defined by so it is the (signed) area enclosed by the curve y=1/x, the x-axis, and the lines x=1 and x=a. If a>1 then lna>0, and if a< 1 then lna< 0. Also ln 1=0. The natural logarithm is related to the exponential function by exp(lnx)=x for all x>0 and ln{exp(x)}=x for all values of x. It is also referred to as the logarithm to base e. For historical reasons a natural logarithm is sometimes referred to as a Napierian logarithm, after the Scottish mathematician John Napier (1550–1617).

Subjects: Probability and Statistics.


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