Tagged Questions
2
votes
1answer
39 views
determining sign of function containing logarithm.
I would like to know the sign of the following term in general. I tried approximately and it was negative. Is there any $m_0$ such that for all $n>m>m_0$, the following function is positive or ...
1
vote
0answers
28 views
What's the most straight forward way to show that a function is increasing?
I am trying to show that:
$$\frac{2}{n}\log\Gamma(\frac{x}{2}) - \log\Gamma(\frac{x+n-1}{n})$$
is an increasing function for $x \ge 5$ and $n > 2$
One way to do this would be to show that ...
1
vote
1answer
68 views
Comparing rates of change: which function increases faster?
I am comparing two functions for $x \ge 1$:
$$f(x) = \ln(\lfloor\frac{x}{9}\rfloor!) - \ln(\lfloor\frac{x}{10}\rfloor!) - \ln(\lfloor\frac{x}{90}\rfloor!)$$
$$g(x) = (2.07766)\sqrt{\frac{x}{9}} + ...
1
vote
2answers
51 views
Logarithm calculation result
I am carrying out a review of a network protocol, and the author has provided a function to calculate the average steps a message needs to take to traverse a network.
It is written as ...
0
votes
1answer
30 views
Function design: a logarithm asymptotic to one?
I want to design an increasing monotonic function asymptotic to $1$ when $x\to +\infty $ that uses a logarithm.
Also, the function should have "similar properties" to $\dfrac{x}{1+x}$, i.e.:
...
1
vote
1answer
42 views
Expansion of Lambert $W$ for negative values [duplicate]
What is a good approximation for the Lambert $W(x)$ function for values between $\frac{-1}{e}$ and $0$? Is it simply $x-x^2$? If so, what bounds are there on the error?
2
votes
0answers
110 views
Log-concave functions whose sums are still log-concave: possible to find a subset?
Rationale:
I am puzzled by a problem of log-concavity, which arises in population dynamics where the curvature of the logarithm of sums is a quantity of interest.
It is well-known that sums of ...
0
votes
2answers
46 views
For what $f(n)$ does $O(f(n) \log n)=O(\log\log n)$?
$k=f(n)$.
Given $O(k \log_2 n)$, what function $f$ of $n$ would be needed for it to equal $O(\log_2 \log_2 n)$?
(where $k \in n \in \mathbb{Z}^+$)
1
vote
2answers
62 views
Derivative for log
I have the following problem:
$$
\log \bigg( \frac{x+3}{4-x} \bigg)
$$
I need to graph the following function so I will need a starting point, roots, zeros, stationary points, inflection points ...
2
votes
1answer
19 views
Estimation for large $k$.
I have a function $f(k)$ defined on the set of natural numbers and I managed to show that $f(k)>n-\binom n k(1-n^{-2/3})^{k(k-1)/2}$ for all integers $n\ge k$. I am hoping to get a further ...
2
votes
3answers
298 views
The relation between an exponential function and a logarithmic function
I have been told multiple times that the logarithmic function is the inverse of the exponential function and vice versa. My question is; what are the implications of this? How can we see that they're ...
0
votes
2answers
92 views
How have they simplified this function?
I have been trying to figure out how the following has been simplified, but I am getting nowhere with it. Anyone have any ideas?
$9(n/3)^{5/2}$ to $(1/3)^{1/2} f(n)$
It is given that $f(n) = ...
1
vote
1answer
74 views
Finding the Function to a log-log plot
My maths is not very good, so please bare with me if the answer is obvious. I have a log-log plot below, which I have generated in R.
I now need to find what i believe to be called the inverse to ...
0
votes
1answer
52 views
Could you describe this function as “logarithmic”?
Consider the following function:
$$f(x) = \frac{1}{\sqrt{x}}$$
As $x$ increases, the value of $f(x)$ decreases, but the decrease tapers off quickly as $x$ gets larger, and if you plot the graph of ...
0
votes
1answer
83 views
Can $2^n$ + $2^m$ be expressed as $2^x$
Can $2^n$ + $2^m$ be expressed as $2^x$ where $x$ is a function of $n$ & $m$?
I'm sure that this would require logarithms to find the answer but my maths is very rusty. Can anyone point me at the ...
