What is the natural logarithm?

Natural logarithm is a logarithm with the base e . The logarithm was invented by Scottish mathematician John Napier (1550-1617). Although it did not represent the concept of natural logarithm itself, this function is sometimes called Napierian Logarithm. Natural logarithm is used in many scientific and engineering applications. English translations are "ratio" and "numbers". Napier spent 20 years working on his logarithms theory and published his work in the book Mirifici logarithmorum canonis descriptio in 1614. The English translation is a description e (x), but the standard notation is f (x) = ln (x).

The domain of natural logarithm is (0, infinity) and the extent is (-Infinity, infinity). The graph of this function is concave, pointing down. The function itself grows, continuous and individual.

Natural logarithm 1 equals 0. Assuming that A and B are positive numbers, then ln (a*b) equals ln (a) + ln (b) and ln (a/b) = ln (a) - ln (b). If A and B are positive numbers A n is a rational number than LN (a n ) = n*ln (a). These properties of natural logarithms are characteristic of all logarithmic functions.

The actual definition of the natural logarithmic function can be found in integral 1/t dt. Integral is from 1 to x S x> 0. Euler number, e , indicates a positive real number by integral 1/t dt from 1 to e The number is an irrational number and is approximately 2.718285.

The natural logarithmic function derivative is 1/x. The derivative with regard to X inverse logarithmic functions, the natural exponential function, is surprisingly a natural exponential function again. In other words, the natural exponential function is its own derivative.