Self doubt algorithms

Question

In coremen it is given that

$\log^kn$=$(\log n)^k$

$\log\log n$ is not equal to $\log^2n$ i understood it with example

please correct me if I am wrong .

Comments

You are right Prince Sindhiya

log^k n=(log n)^k 

log log n = log(log n)

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As per my knowledge,

 

log^k ( n ) = log ( log ( log .... ( log n ) ) ) ------------------------ ( log applied k times )  is TRUE

 

log^k ( n ) =  ( log n )^k ------------------------ is FALSE

 

log^k ( n ) =  ( log n )^k  given in cormen

@ Prince Sindhiya, where it given, can you tell the page number.

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Page no. 56

Answer 1

Usually f^2(x)=f(f(x)) means the composition of f by itself.

However, for some special functions, it is much more common that we want to square it than we want to composite it.

For and the trigonometrical functions, that’s the case, so:

sin^2 (x)=(sin(x))^2=sin(x)⋅sin(x)

log^2 (x)=(log(x))^2=log(x)⋅log(x)

But exp²(x)=exp(exp(x))