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Natural logarithm is the base logarithm e (mathematical constant, approximately equal to the number 2.718281828459…).
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Definition of natural logarithm
When e y = x, the natural logarithm (ln) of the number x as follows:
ln (x) = loge(x) = y
Relationship with the exponential function
The function is logarithm ln (x) is the inverse of the exponential function ex.
For х > 0,
f (f -1(x)) = eln (x) = x
or
f -1(f (x)) = ln(ex) = x
Properties of the natural logarithm
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| Property | Formula | Example | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| multiplication logarithm | division logarithm | Logarithmic degrees | root logarithm | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Derivative of the logarithm | Integral logarithm | Logarithm of a negative number | Logarithm of a complex number | Logarithm of infinity | Euler identity | Таблица натуральных логарифмов
natural log graphThe natural logarithm function is given as y = ln x. Exists only for non-negative values of the variable x. The chart looks like this:
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