# Tagged Questions

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### What algorithm solves this problem? Non-linear measuring tape

A measuring tape is marked at 0, 5, 15 and 40. The distances between each mark are marked on top. At what distances should I mark 1 through 4, as well as 6-14 and 16-39? My math knowledge does not ...
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### Logarithm Base Question

Suppose you have a integer n. Log2(n) is supposed to be ~ the number of times you have to divide n by 2 until you reach one. Now let's say you want to know ~ the number of times you have multiply n by ...
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### How is $O(\log(\log(n)))$ also $O( \log n)$?

How is $O(\log(\log(n)))$ also $O( \log n)$? I have seen this result somewhere with this but I still didn't quite understand how this is true. This would also help me compute Big Omega of the ...
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### Base of logarithm decrease when variable count increase

I run a large online platform where users submit articles and earn points. I am working on an algorithm where the more comments they submit, the higher score they will receive. In its simplest ...
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### How to generate $\log$ function that intersects at $(0,1)$ and $(1,0)$?

I apologize for any incorrect or missing formatting, first time posting in the math stack exchange. It's been a few years since I've done any kind of calculus, so I remember nothing at all, which is ...
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### Using math functions to time finales of a fireworks show

This year, I have the honor of programming two finales for a fireworks show. I want to use math. I suspect that I should use a function such as square root or log to specify the decreasing pause ...
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### Logarithm of $\frac{a^k}{a^k-1}$

On a question on this site there is an explanation of the algorithm Knuth gives in The Art Of Computer Programming to compute an approximation of $y = \log_bx$. Now, I understand why it works; ...
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### Prove that $\log n = O(\log^2 n)$

Trying to solve this, but I can't seem to figure it out. Its fairly straight forward.
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### How do you solve a equation by converting to logarithm form for the problem$3e^{x-4} +2=83$?

$3e^{x-4} +2=83$ I understand converting logarithms but i dont understand how to convert e into log form and solve. help would be deeply appreciated.
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### merge sort vs insertion sort time complexity

How do I solve exercise 1.2-2 from Introduction to Algorithms 3rd Edition, Author: Thomas H. Cormen Would I need to set both sides equal to each other and solve for n?
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### Calculating an exponentially increasing vector of points in a test and measure system

My application is setting and measuring current and voltage in a physical system with a software algorithm. Given these parameters: min, ...
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### Diffie hellman and the discrete algorithm problem

Suppose Alice and Bob are exchanging keys using Diffie-Hellman Key-Exchange Algorithm. a - Alice secret key g - generator p - prime x - the public key passed from Alice to Bob. Eve is listening to ...
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### Why does the method to find out log and cube roots work?

To find cube roots of any number with a simple calculator, the following method was given to us by our teacher, which is accurate to atleast one-tenths. 1)Take the number $X$, whose cube root needs ...
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### How do I go about manipulating this summation equation to solve it?

In my textbook, Introduction to Algorithms, the following is shown: And I believe I understand that. However, I have a similar equation to the one on the first line, but instead of ...
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### How does my professor go from this logarithm to the next?

In the above picture, how does he go from the third-last line to the second last?
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### Inequality $C\lceil\log{n}\rceil! \geq n^k$

I've been struggling to prove there exist $C$ for $n, n_{0}, \forall k >0 \in \mathbb{R}$ such that $\forall n > n_{0}$: $$C\lceil\log{n}\rceil! \geq n^k$$ As you ...