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Nov 7, 2018 at 22:13. 5. "To log in" and "to log into" are Reflexive Separable Phrasal Verbs which often have the reflection omitted. They mean the same thing but have slightly different grammatical construction. "To log in" requires a prepositional phrase to describe what a person is logging into.
To remember log(1 − x) l o g (1 − x) just do log(1 − x) = − ∫ dx 1 − x = − ∫(1 + x + x2 + ⋯)dx = − (x + x2 2 + x3 3 + ⋯) = − ∞ ∑ n = 1xn n. l o g (1 − x) = = = = − ∫ d x 1 − x − ∫ (1 + x + x 2 + ⋯) d x − (x + x 2 2 + x 3 3 + ⋯) − ∑ n = 1 ∞ x n n. – Kian. Commented May 2, 2015 at 16:15. Is ...
the Taylor series for ln (x) is relatively simple : 1/x , -1/x^2, 1/x^3, -1/x^4, and so on iirc. log (x) = ln (x)/ln (10) via the change-of-base rule, thus the Taylor series for log (x) is just the Taylor series for ln (x) divided by ln (10). – correcthorsebatterystaple. Mar 18 at 14:35.
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$\begingroup$ As an aside, to make matters worse, some authors will write $\log$ without a subscript and mean different things than one another.
2. There is currently no well-known function f(x, y) f (x, y) such that log(x) ⋅ log(y) = log(f(x, y)). log (x) ⋅ log (y) = log (f (x, y)). That is, the function f(x, y):= xlog(y) = ylog(x) f (x, y):= x log (y) = y log (x) has not been given a name yet, although it is a valid function. This situation may change at some future time.
For my money, log on to a system or log in to a system are interchangeable, and depend on the metaphor you are using (see comment on your post). I suppose there is a small bit of connotation that "log on" implies use, and "log in" implies access or a specific user.
$\begingroup$ If so: no. Changing the base of the logarithm will make a difference by a constant factor; while $\log_2\log_2 x$ is exponentially smaller than $\log_2 x$. $\endgroup$ – Clement C. Commented Mar 6, 2017 at 19:24
$\log (x)$ refers to $\log_2 (x)$ in computer science and information theory. $\log(x)$ refers to $\log_e(x)$ or the natural logrithm in mathematical analysis, physics, chemistry, statistics, economics, and some engineering fields. $\log(x)$ refers to $\log_{10}(x)$ in various engineering fields, logarithm tables, and handheld calculators.
The meaning is defined as follows: the logarithm of x to the base b (denoted by logb(x)) is the exponent to which b needs to be raised to obtain x. That is, if y = logb(x), then x = by. By convention, the "natural logarithm" is the logarithm to the base e, where e is Euler's constant: ln(x) = loge(x). Share.