# Tagged Questions

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### What does this log notation mean?

Can someone please explain what $^2\log x$ means? Is it the same as saying $\log x^2$ or is it something completely different? Here is an image of it as an example:
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### (log n)^k = O(n)? For k greater 1

$$(\log n)^k = O(n)?$$ For $k> 1$. $k$ is a constant, such as number $4$. I think it is not true for $n=32$ and greater. $n=32, n=64, n=128,\dots$ So, I can not find $n_0$ and $c$.
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### Notation of logarithm and its exponent

I am little confused about this notation, $\log^3 n$. Does it mean $(\log n)^3$ or $\log (\log (\log n))$?
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### When log is written without a base, is the equation normally referring to log base 10 or natural log?

For example, this question presents the equation $$\omega(n) < \frac{\log n}{\log \log n} + 1.4573 \frac{\log n}{(\log \log n)^{2}},$$ but I'm not entirely sure if this is referring to log base ...
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### little o notation with natural logs

I'm having trouble with little o notation. Help me show that: $2(n^2 + 100n)\log^5n = o(n^2\sqrt{n})$. It is the last hwk on my sheet and I don't understand it, if someone can help me with ...
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### Two $\psi$ functions

This is either a notation/history question or a point of confusion. In (for example) Ramanujan's proof of Bertrand's postulate, he uses the following notation: $\log [x]!$ means $\log ([x]!),$ in ...
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### How should “7 $\log_{10}$” be interpreted?

A cookery related article I want to refer to mentions a "7 log10 relative reduction of salmonella". A few related sources suggest this evaluates to 10,000,000, although I would have imagined that 107 ...
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### Why 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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### What does $\log^{2}{x}$ mean?

What is it used for and why doesn't it equal $\large\log{x^2}$?
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### Notation question: $x\ln^2(1000/y)$ into MATLAB

I've been tasked with working out how much some incorrectly entered calibration coefficients have affected some measurements we've taken. I have the algorithm used, which I can use to work backwards ...
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### Alternative notation for exponents, logs and roots?

If we have $$x^y = z$$ then we know that $$\sqrt[y]{z} = x$$ and $$\log_x{z} = y .$$ As a visually-oriented person I have often been dismayed that the symbols for these three operators ...
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### How did the notation “ln” for “log base e” become so pervasive?

Wikipedia sez: The natural logarithm of $x$ is often written "$\ln(x)$", instead of $\log_e(x)$ especially in disciplines where it isn't written "$\log(x)$". However, some mathematicians ...