Tagged Questions
0
votes
1answer
55 views
Smallest Mersenne prime with 100 million digits?
As some of you are probably aware, the Great Internet Mersenne Prime Search (GIMPS) is managing the search for the largest Mersenne primes of the form $M_p=2^p-1$, where $p$ is itself prime (GIMPS ...
1
vote
1answer
47 views
Calculating how long it will take for the half-life of X amount to fall below Y amount
I am trying to determine how long it will take ($t$) for the half life of 500 amount of substance to fall below 100 (to be $\le$ 99 -- I am only concerned with integers) when it has a half life of 5.
...
6
votes
3answers
122 views
Apparently cannot be solved using logarithms
This equation clearly cannot be solved using logarithms.
$$3 + x = 2 (1.01^x)$$
Now it can be solved using a graphing calculator or a computer and the answer is $x = -1.0202$ and $x=568.2993$.
But ...
0
votes
2answers
86 views
Logarithmic Number System Addition
Can somebody explain in simple terms how addition works in a logarithmic number system.
Say I have the numbers A and B. These are logarithms (base e, say) of the actual quantities they represent. They ...
0
votes
1answer
90 views
Number of digits in base 10=9+1
Let $\tau:\mathbb N\to\mathbb N$ be the function that counts the number of digits of an nonnegative integer, i.e. $\tau(x)$ is the number of digits of $x$ in base 10. For example $\tau(5)=1$, ...
1
vote
1answer
62 views
Use identities to simplify $lg(a^2+b^2)^2$
Use logarithmic identities to simply the following:
$$lg(a^2+b^2)^2$$
I started with
\begin{eqnarray}
lg(a^2+b^2)^2&=&2 \cdot lg(a^2+b^2) \\
\end{eqnarray}
I think it's not the final ...
0
votes
2answers
107 views
How ${\left(\frac 12 \right)}^{{\lg n}}$ = ${\frac 1n}$ for any natural number $n$?
Consider binary logarithm . How is the value of ${(\frac 12 )}^{{\lg n}}$ = ${\frac 1n}$?
I was going through this video of skiplists and the professor at 53:22 seconds make this claim .
1
vote
4answers
137 views
What is the $(\lg n)$-th root of $n$?
I am looking for the answer of the $(\lg n)$-th root of $n$, that is, $\sqrt[\lg n]{n}$. What is the answer and what log property should I use here? Please assume base as $2$ and $n$ as a natural ...
0
votes
3answers
303 views
arithmetic progression involving logarithm
$\log_2 X$, $\log_2 (X+9)$ and $\log_2(X+45)$ are 3 consecutive terms of an arithmetic progression; find
$\qquad$(i) the value of X;
$\qquad$(ii) the first term and the common difference; and
...
1
vote
1answer
82 views
Number of digits in different number systems?
I know a similar question was asked before, but I wanted to know if this can be extended to any number system by a generic formula.
For example, given a number X in number system A, how many digits ...
2
votes
2answers
120 views
difference of logs
$\log(a - b) - \log(a - c)$
Does this have a simpler form? Perhaps one where the $a$s have cancelled out? I know it can also be expressed as a log of the fraction: $\log\frac{(a-b)}{(a-c)}$, but the ...
