Solve for $m$ in $d^m = n$

Question

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

Can anyone help me?

Answer 1

Using any logarithm $\log$, we have $$\log n = \log (d^m) = m \log d,$$ so $$m = \frac{\log n}{\log d} = \log_d n.$$

Answer 2

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