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- Natural_logarithm abstract "The natural logarithm of a number is its logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x) or log(x). This is done in particular when the argument to the logarithm is not a single symbol, to prevent ambiguity.The natural logarithm of x is the power to which e would have to be raised to equal x. For example, ln(7.5) is 2.0149..., because e2.0149...=7.5. 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 area being taken as negative when a<1). The simplicity of this definition, which is matched in many other formulas involving the natural logarithm, leads to the term "natural". The definition of the natural logarithm can be extended to give logarithm values for negative numbers and for all non-zero complex numbers, although this leads to a multi-valued function: see Complex logarithm.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:Like all logarithms, the natural logarithm maps multiplication into addition:Thus, the logarithm function is an isomorphism from the group of positive real numbers under multiplication to the group of real numbers under addition, represented as a function:Logarithms can be defined to any positive base other than 1, not just e. However, logarithms in other bases differ only by a constant multiplier from the natural logarithm, and are usually defined in terms of the latter. For instance, the binary logarithm is just the natural logarithm divided by ln(2), the natural logarithm of 2. Logarithms are useful for solving equations in which the unknown appears as the exponent of some other quantity. For example, logarithms are used to solve for the half-life, decay constant, or unknown time in exponential decay problems. They are important in many branches of mathematics and the sciences and are used in finance to solve problems involving compound interest.".
- Natural_logarithm thumbnail Log.svg?width=300.
- Natural_logarithm wikiPageExternalLink demystifying-the-natural-logarithm-ln.
- Natural_logarithm wikiPageID "21476".
- Natural_logarithm wikiPageRevisionID "606265109".
- Natural_logarithm hasPhotoCollection Natural_logarithm.
- Natural_logarithm subject Category:E_(mathematical_constant).
- Natural_logarithm subject Category:Elementary_special_functions.
- Natural_logarithm subject Category:Logarithms.
- Natural_logarithm comment "The natural logarithm of a number is its logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x) or log(x).".
- Natural_logarithm label "Logarithme naturel".
- Natural_logarithm label "Logaritmo natural".
- Natural_logarithm label "Logaritmo natural".
- Natural_logarithm label "Logaritmo naturale".
- Natural_logarithm label "Logarytm naturalny".
- Natural_logarithm label "Natural logarithm".
- Natural_logarithm label "Natuurlijke logaritme".
- Natural_logarithm label "Натуральный логарифм".
- Natural_logarithm label "لوغارتم طبيعي".
- Natural_logarithm label "自然対数".
- Natural_logarithm label "自然對數".
- Natural_logarithm sameAs Logaritmo_natural.
- Natural_logarithm sameAs Logarithme_naturel.
- Natural_logarithm sameAs Logaritma_natural.
- Natural_logarithm sameAs Logaritmo_naturale.
- Natural_logarithm sameAs 自然対数.
- Natural_logarithm sameAs 자연로그.
- Natural_logarithm sameAs Natuurlijke_logaritme.
- Natural_logarithm sameAs Logarytm_naturalny.
- Natural_logarithm sameAs Logaritmo_natural.
- Natural_logarithm sameAs m.05d2y.
- Natural_logarithm sameAs Q204037.
- Natural_logarithm sameAs Q204037.
- Natural_logarithm wasDerivedFrom Natural_logarithm?oldid=606265109.
- Natural_logarithm depiction Log.svg.
- Natural_logarithm isPrimaryTopicOf Natural_logarithm.
