Proving the Log of a Power Rule: log(n^k) is O(log(n)) for any constant k > 0

[Gear2d]

I was wondering how would I go about proving the Log of a Power Rule:

log(n^k) is O(log(n)) for any constant k > 0

 

[statdad]

Think of a basic property of logarithms

 

[mistermath]

You should show what you've tried, but basically..

log (n^k) = k log (n), and use w/e technique you want to show the constant up front does not matter.

OR are you asking how to prove the power rule for logs? I'll give a hint..

log (x) = y <=> 10^y = x

(assuming log has base 10 and <=> means if and only if).

 

[Gear2d]

You should show what you've tried, but basically..

log (n^k) = k log (n), and use w/e technique you want to show the constant up front does not matter.

OR are you asking how to prove the power rule for logs? I'll give a hint..

log (x) = y <=> 10^y = x

(assuming log has base 10 and <=> means if and only if).

I see what you are saying when log (n^k) = k log (n) which is O(log (n)) based on Coefficient Rule ( http://www.augustana.ca/~hackw/csc210/exhibit/chap04/bigOhRules.html ). But, I am trying to prove the power rule for logs. Just don't know how to approach it or where to start off. And the log is base 2 and not 10 (sorry for got to mention that).