I believe the answer is $m = \lceil \sqrt[d]n \rceil$ or $\lfloor \sqrt[d]n \rfloor$.
Can anyone help me?
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1$\begingroup$ Have you heard of logarithms? $\endgroup$ – String Jan 22 '15 at 2:37
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$\begingroup$ ahahah this made me laugh, what apositive community! $\endgroup$ – Bauer Jan 22 '15 at 3:31
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$\begingroup$ That is the danger of written communication. My comment was merely a question to get the exchange started, but if read as a sarcastic comment regarding your mathematical knowledge it may seem a bit harsh, I agree :) $\endgroup$ – String Jan 22 '15 at 4:30
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Using any logarithm $\log$, we have $$\log n = \log (d^m) = m \log d,$$ so $$m = \frac{\log n}{\log d} = \log_d n.$$
answered Jan 22 '15 at 2:38
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Try using logarithms. A logarithm is defined as follows,
If $a^{b}=c$, then $\log_{a} c=b$
So, similarly, here we get
$m=\log_{d} n$.
We can further simplify it by changing the logarithms' base to $10$,
$m=\frac{\log_{10} n}{\log_{10} d}$
If you want to learn more about logarithms, go here
