All Questions
10
questions
0
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2
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897
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Determine all integers n>1 such that every power of n has odd number of digits.
I know that the number of digits in a number is equal to the integer part of the common logarithm of that number plus one. For example, log10(100) is 2 and the number of digits is 3.
I tried to solve ...
2
votes
0
answers
39
views
Does every basic exponent property have a corresponding logarithm property and vice versa?
Here is what I'm referring to:
For $0 < a \neq 1$, $\,0 < b \neq 1$, and $m,n \in \mathbb{R^+}$, $p = a^m$, $q = a^n,$
$$\begin{align*}
a^0 &= 1 \qquad &\qquad \log_a(1) &= 0 \tag{a}\...
- 287
1
vote
1
answer
50
views
Basic calculation issue
So this problem seems rather elementary however I can't reach the solution given in my notes so I was hoping someone here may be able to enlighten me. (I'm finding confidence intervals for Survival ...
1
vote
1
answer
50
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Simplifying $e^{-R/8300} = e^{-T/8300}(1-e^{-2.996(5000-T)/1000})$
I'm here asking this question simply to know how this author derived his answer in the article "Correlation of C-14 Age with the Biblical Time Scale" (PDF link via grisda.org).
Solution 2 ...
- 21
0
votes
1
answer
60
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How to solve a root (eg, $x^{1/3}$) using arithmetic but without using a power?
How can I use the exponential constant and the natural logarithm operation, to express a "root" operation?
Example: $x^{1/3}$.
Is there a combination of operations that are only arithmetic,...
- 137
1
vote
1
answer
53
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Decomposing fractions
I am not sure how these two terms are equal from this wiki:
$$
I(X,Y) = KL(p(x,y) || p(x)p(y)) = \sum_{x,y}p(x,y) \log[\frac{p(x,y)}{p(x)q(y)}] \\
I(X,Y) = \sum_{x,y}p(x,y) \log[\frac{p(x,y)}{p(y)}...
- 736
0
votes
3
answers
519
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The first three terms of a geometric sequence are 3,9,27. Find the first term in the sequence which exceeds 500
Now do you have to use trial and error for this kind of problem?
- 61
2
votes
1
answer
101
views
What happens when you calculate $\log$ of a $\log$?
I need to find out an estimation or any bounds for what $\log(k)$ is when $k = \lceil \frac{n}{2\log(n)} \rceil$.
I have reached a point in my calculations where I am left with
$\left( \frac{n - \...
- 31
1
vote
1
answer
29
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Logarithmically bounded function fulfills $f(n) \le \lceil m \cdot \log_b r \rceil$ for certain numbers $n,m,r$
Let $f : \mathbb N \to \mathbb N$ be a function such that $f(n) \le 1 + \log_b n$ for some base $b$ and all $n$. Now let $n \in \mathbb N$ have the property that
$$
\frac{r^m - 1}{r-1} \le n < \...
- 18.2k
1
vote
2
answers
96
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Show $n \cdot \log_b r + \log_b \frac{r}{r-1} \le \lceil n \cdot \log_b r \rceil$
Let $n$ be a natural number and $b, r > 1$ be two natural numbers, then I guess we have
$$
n \cdot \log_b r + \log_b \frac{r}{r-1} \le \lceil n \cdot \log_b r \rceil.
$$
where $\lceil x \rceil = \...
- 18.2k