2
votes
1answer
57 views

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:
0
votes
1answer
38 views

(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 $c$.
0
votes
2answers
115 views

Notation of logarithm and its exponent

I am little confused about this notation, $\log^3 n$. Does it mean $(\log n)^3$ or $\log (\log (\log n))$?
1
vote
2answers
80 views

Deriving logarithmic identities

Wikipedia says: The numerical value for logarithm to the base $10$ can be calculated with the following identity: $$\mathrm{log_{10}}(x) = \frac{\mathrm{ln}(x)}{\mathrm{ln}(10)} \\ ...
3
votes
2answers
132 views

Meaning of $\log$

If you write $\log{x}$ rather than ${\log_a{x}}$ for some base $a$, does it have a particular meaning? Sometimes I see people leave off the base by mistake when posting questions and it seems from the ...
0
votes
3answers
100 views

Question about changing a logarithm's base

I've been using the following method to derive/remember the logarithm base conversion formula: If I want to convert $\log_a(x)$ to an expression in base $b$, I say, $$a^{\log_a(x)}=x\\ ...
16
votes
3answers
2k views

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 ...
1
vote
1answer
190 views

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 ...
0
votes
1answer
80 views

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 ...
4
votes
2answers
201 views

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 ...
13
votes
8answers
847 views

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: $$\log_2 8=x$$
4
votes
2answers
743 views

What does $\log^{2}{x}$ mean?

What is it used for and why doesn't it equal $\large\log{x^2}$?
0
votes
2answers
247 views

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 ...
14
votes
11answers
1k views

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 ...
18
votes
8answers
3k views

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 ...