- published: 11 Nov 2011
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The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828. The natural logarithm is generally written as ln(x), loge(x) or sometimes, if the base of e is implicit, as simply log(x).
The natural logarithm of a number x is the power to which e would have to be raised to equal x. For example, ln(7.389...) is 2, because e2=7.389.... The natural log of e itself (ln(e)) is 1 because e1 = e, while the natural logarithm of 1 (ln(1)) is 0, since e0 = 1.
The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a. The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, leads to the term "natural." The definition can be extended to non-zero complex numbers, as explained below.
The natural logarithm function, if considered as a real-valued function of a real variable, is the inverse function of the exponential function, leading to the identities:
I don't wanna work all day
I don't wanna dress in grey, no
I used to be keen, the brightest boy in school
Now it's all through, 'cause I'm lonely without you
I don't wanna work all day
I don't wanna dress in grey, no
I used to be keen, the brightest boy in school
Now it's all through, 'cause I'm lonely without you
It's just another
It's just another
Another lonely schoolday
It's just another
It's just another
Another lonely schoolday
I don't wanna work all day
I don't wanna make the grade, no
I used to be keen, the brightest boy in school
Now it's all through, 'cause I'm lonely without you
Yeah - yeah, yeah - yeah