# Questions tagged [number-comparison]

Tag for problems about comparing explicitly given numbers, often by hand calculation only.

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### Proving $3^{100} > 5\cdot10^{47}$ with integral representation

I want to prove that $3^{100} > 5\cdot10^{47}$ without using calculator or any approximation of the logarithm. I tought about finding an integral representation of $(3^{100} - 5\cdot10^{47})$ with ...
• 743
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• 181
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### Show that $\sqrt{10}+\sqrt{26}+\sqrt{17}+\sqrt{37} \gt \sqrt{341}$

Show that $\sqrt{10}+\sqrt{26}+\sqrt{17}+\sqrt{37} \gt \sqrt{341}$. This is inspired by Showing $x+y>z$, where $x=\sqrt{10}+\sqrt{26}$, $y=\sqrt{17}+\sqrt{37}$, and $z=\sqrt{323}$. Is my idea ...
• 108k
1 vote
64 views

### Comparing log with rationals [closed]

So I came across with this problem: To prove $\log_27<2\sqrt3$. This is not difficult as LHS$<3<$RHS. However, I did want to know how to generalise the solution. In particular, given integers ...
• 49
1 vote
44 views

### Inequality using order relation

$1^{2n} +2^{2n} +3^{2n} \ge 2\times 7^n$ This question is from An excursion in mathematics in the section of order relation I tried using induction,tried to prove $1^{2n} +2^{2n+1} \ge 2\times 7^n$ ...
74 views

### Compare $A$ and $B$ [closed]

Compare $A$ and $B$ with: $$A = \sqrt{2017} + \sqrt{2019} + \sqrt{2023}$$ $$B = \sqrt{2018} + \sqrt{2020} + \sqrt{2021}$$ I tried to prove $A^4 < B^4$ but it's too hard to do that.
1 vote
71 views

24 views

### What is the best-case number of array item comparisons in this algorithm, in terms of n?

The Smart Bubble Sort. Preconditions: x1, x2, ... , xn is in U, a set that is totally ordered by <, and n ≥ 2. Postconditions: x1 ≤ x2 ⋯ ≤ xn. ...
93 views

### Percentage question in GRE

Ashley's score was 20% higher than Bert's score. Bert's score was 20% lower than Charles Score. Is Ashley's score greater than Charles Score? This is essentially a GRE question however my mind can not ...
• 1
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### Comparing $(2n)^{\ln {n}}$ to $(\ln{n})^{2n}$ for $n > 1000$ [closed]

I want to compare these two numbers and prove which is bigger for $n > 1000$: first: $(2n)^{\ln {n}}$ second: $(\ln{n})^{2n}$ I tried to somehow simplify them to similiar form and do induction, but ...
989 views

### Prove that: $e-\ln(10)>\sqrt 2-1.$

The author's original inequality is as follows. Prove that: $$e-\ln(10)>\sqrt 2-1$$ Is there a good approximation for $$e-\ln 10?$$ Actually, I am also wondering that, Where does $\sqrt 2-1$ come ...
• 1,671
1 vote
51 views

### Method for finding the largest positive difference between two pairs of IEEE 754 double precision floating point numbers and fixed-point numbers

I have two pairs of IEEE 754 double precision (64-bit) floating-point numbers and unsigned fixed-point numbers, and I'm trying to find which pair has the greatest difference. The fixed-point numbers ...
• 295
1 vote
51 views

### comparison with logic problems

I am a bit confused regarding the logic combined with size comparisons. For example, if there is a statement x > y -> x >= y I believe that this would be ...
31 views

### How do I determine how similar the angles of a triangle are to a given triangle? [closed]

I am trying to determine how close a triangle is to a given known triangle based on the angles. I know the 3 angles of a TRUTH triangle. I know the 3 angles of an INPUT triangle. I want to determine a ...
• 149
138 views

### What is the easiest way to compare $\log_2 (72)$ with $2\pi$?

I need to compare $\log_2 (72)$ with $2\pi$. What is the easiest way to do it?
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• 9,206
1 vote