How would I go about finding the upper and lower bounds of $T(n) = 9T(n/81)+\log(n)$?
Give asymptotic upper and lower bounds for $T(n)$ in: $T(n) = 9T(n/81)+\log(n)$
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discrete-mathematics
recurrence-relations
asymptotics
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0One approach is to take $a_n = T(81^n)$ then $a_{n+1} = 9 a_{n} +n \log(81)$ which is a recurrence relation you can solve and then take $n = \frac{\log(m)}{\log(81)}$ to get $T(m)$. The simpler approach is to apply the [master theorem](https://en.wikipedia.org/wiki/Master_theorem#Generic_form). – 2017-01-15
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0Show what you tried? – 2017-01-15