# Tagged Questions

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### Is there a simple algorithm for exponentiating large numbers to large powers?

I've been thinking about this for some days, a multiplication is a lot of sums, so: $$75\times 75=\overbrace{75+75+75+75+75+75+75+75+\cdots}^{\text{75 times}}$$ But then, there is a simple algorithm ...
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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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### Is there any simple method to calculate $\sqrt x$ without using logarithm

Suppose that we don't know logarithm, then how we would able to calculate $\sqrt x$, where $x$ is a real number? More generally, is there any algorithm to calculate $\sqrt [ n ]{ x }$ without using ...
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### 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 .
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### 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 ...
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### 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 ...
$\log(a - b) - \log(a - c)$ 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 ...