+2864 What integer n has the property that \(5^{96}\) is greater than \(n^{72}\) and \(5^{96}\) is less than \((n+1)^{72}\).
So I did
5^96>n^72
5^96<(n+1)^72
Then take 12th root
5^8>n^6
5^8<(n+1)^6
Then I take square root
5^4>n^3
5^4<(n+1)^3
Then I easily deduced that n must be 8.
Is my solution correct?
+118687 I am not saying that your answer is wrong CalculatorUser BUT did you consider the possibility that n could be negative?
+118687 I know that is right Alan and I think CalculatorUser does too, he wanted to do it without the calc I think.
BUT I just wanted him/her to think about wether there could be a negative answer.
I know the answer to this, I just want to be sure that CalculatorUser has thought about it too.
+2864 Yes thank you, Melody, I never thought that my answer could be negative. I am lucky that the problem only had one answer.
Next time in these problems, I will make sure there are no negative answers
+118687 I suggest you think very hard about THIS answer/question
You should not just accept what some answer written down somewhere is.
How do you know there is not a negative answer? Answer: Someone told you so.
Well that is not you knowing, that is at best someone else knowing.
If you think about it purely as a logic exercise, you will work out why there cannot be a negative answer.
I took me a while to get my head around it so it might take you a while too but the reason is not very complex. 
