Question

which of the following is correct?

Comments

I think 1st one is correct and 2nd one is incorrect ....

take a small example .......

(log2^8)^2 = 64

but

loglog2^8 = 3

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It is definition specific . Different author use different notation .

Answer 1

obviously 1st one is correct.basic arithmetic question . Refer  any 10 std maths book

Comments

Thank you :)

 since I have no 10 std maths book to refer,the 2 answer given here  http://math.stackexchange.com/questions/159720/how-to-solve-this-recurrence-tn-2tn-2-n-log-n helped me

Answer 2

2nd one is correct..

Comments

yeah second one is right !

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@  spriti1991 

I think i)  is correct. sumit kumar said refer any 10 th std maths text.If you didn't have 10 th std text then I will help you :)

please solve T(n)=2T(n/2)+nlogn using master theorem.We will get http://math.stackexchange.com/questions/159720/how-to-solve-this-recurrence-tn-2tn-2-n-log-n as shown in 2 nd answer.solve same recurrence relation using substitution we will get nT(1)+n((log(n)(1+log(n)))/2)=Θ(n*logn*logn) as shown in 1st answer

so i) is correct 

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Yeah anu :) I will look after it Thanks :)

Answer 3

definately first one is correct...

log^k (n) = (log n)^k  

log .log n = log (logn)