Answer by MJD for Why does the logarithm require a special notation?
While pondering the possibility of a less specialized notation, I thought of a specific advantage possessed by the $\log$ notation: it leaves the base of the logarithm implicit. You can say, for...
View ArticleAnswer by lhf for Why does the logarithm require a special notation?
One reason is that the logarithm is not an elementary function and so cannot be expressed by a "formula".
View ArticleAnswer by Geoff Robinson for Why does the logarithm require a special notation?
Many texts develop the logarithm function before the exponential function. For example, in M. Spivak's book "Calculus", the function $\log(x)$ is defined for positive $x$ via$\log(x) =...
View ArticleAnswer by hmakholm left over Monica for Why does the logarithm require a...
Having a notation for $\log_2 8$ makes it much easier to express in a succinct way what to do with the solution to the equation after computing it. Writing, say,$$\log_2 x + (\log_2 y)^2$$is shorter...
View ArticleAnswer by Godot for Why does the logarithm require a special notation?
The concept of the logarithm is not just the notation. The logarithm, i.e.a function $\log:\mathbb{R}_{+}\rightarrow\mathbb{R}$, has many usefull properties. The property that made the logarithm so...
View ArticleAnswer by davidlowryduda for Why does the logarithm require a special notation?
Let's come up with a very simple problem.Suppose we wanted to write that $\log_2 8 + \log_3 9 = x$ (here, of course, $x = 5$). What would we write without the logarithm notation? We can't write $2^x +...
View ArticleAnswer by MJD for Why does the logarithm require a special notation?
Suppose you would like to express the fact that, say, $$\lim_{n\to\infty} \left(-\log_e n + \sum_{i=1}^n \frac1i\right) = 0.577\ldots.$$ How do you propose to do this with no $\log$ notation?Here is...
View ArticleAnswer by Michael Greinecker for Why does the logarithm require a special...
I think if you just want to calculate the logarithm of some number with respect to a certain base, your approach works nicely. But we often deal with the logarithm as a function, so often that this...
View ArticleWhy does the logarithm require a special notation?
Since the logarithm is the reversed exponentiation, why does it need a distinct notation for it? Why can't we just ask: $$2^x=8$$Instead of:$$\log_2 8=x$$
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