# Solve for $m$ in $d^m = n$ [duplicate]

I believe the answer is $m = \lceil \sqrt[d]n \rceil$ or $\lfloor \sqrt[d]n \rfloor$.

Can anyone help me?

• Have you heard of logarithms? – String Jan 22 '15 at 2:37
• ahahah this made me laugh, what apositive community! – Bauer Jan 22 '15 at 3:31
• 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 :) – String Jan 22 '15 at 4:30

Using any logarithm $\log$, we have $$\log n = \log (d^m) = m \log d,$$ so $$m = \frac{\log n}{\log d} = \log_d n.$$
If $a^{b}=c$, then $\log_{a} c=b$
$m=\log_{d} n$.
We can further simplify it by changing the logarithms' base to $10$,
$m=\frac{\log_{10} n}{\log_{10} d}$