Because when the system of logarithms with the base 'e' was defined and
tabulated, it was entitled with the identifying label of "Natural Logarithms".
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My improvement: The natural log base is e (a numerical constant of about 2.718). It is chosen as a log base since there is a mathematical series (a "string" of mathematical numerical terms to be summed) for calculating a logarithm (ie. exponent of the base) of a number, which has a base of e. Series for calculating logarithms with bases other than e have basically not been developed.
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log 100 base e = log 100 base 10 / log e base 10 log 100 base 10 = 10g 10^2 base 10 = 2 log 10 base 10 = 2 log e base 10 = 0.434294 (calculator) log 100 base e = 2/0.434294 = 4.605175
Very simple: it is 1.6989700043 to be exact. You can test this because log50 means we assume the natural log (base 10), if you test 10 to the exponent of 1.6989700043 you should render 50 as your result :D
log2x = log x / log 2 On the right side, you can use logarithm in any base (calculators usually provide base-10 and base-e), just be sure to use the same base in both cases. Thus: log2x = ln x / ln 2 or: log2x = log10x / log102
Ever heard of calculator?? log to base 10 = 0.0367087, natural log, 0.08452495
It means the logarithm to the base e. The number "e" is approximately 2.71828... In other words, if you ask, for instance, "what's the natural logarithm of 100", that's equivalent to asking "to what number must I raise 'e', to get the answer 100". The solution of the equation e^x = 100 in this example.