It is usually written using the shorthand notation lnx, instead of logex as you might expect. The natural logarithm of a number x is the logarithm to the base e, where e is the mathematical constant approximately equal to 2.718. Another reason why logarithms to the base e can justly be called natural logarithms is that this system has the simplest derivative of all the systems of logarithms. Natural Logarithms Have Simpler Derivatives Than Other Sys- tems of Logarithms. The natural log simply lets people reading the problem know that you’re taking the logarithm, with a base of e, of a number. In the same fashion, since 102 = 100, then 2 = log10 100. For example, 23 = 8 therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8. How do you calculate logs?Įxpressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459.
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