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Maths-

General

Easy

Question

The expression where $p greater or equal than 2 comma p element of N semicolon n element of N$ when simplified is.

Independent of p
Independent of p and of n
dependent on both p & n
positive

hint Hint:

Using formula , $log subscript a open parentheses b to the power of c close parentheses space equals space c space log subscript a open parentheses b close parentheses right square bracket$ and find the value of given expression in terms of n and p 's .

The correct answer is: Independent of p

= $log subscript p open parentheses p to the power of 1 over p x 1 over p x 1 over p x.... space n space t i m e s end exponent close parentheses space$
$equals space log subscript p open parentheses p to the power of n over p end exponent close parentheses space space left square bracket u sin g comma space log subscript a open parentheses b to the power of c close parentheses space equals space c space log subscript a open parentheses b close parentheses right square bracket equals n over p space log subscript p open parentheses p close parentheses space left square bracket space u sin g comma space log subscript a open parentheses a close parentheses space equals 1 right square bracket equals space n over p$
Therefore, the value of expression is dependent on both n and p.

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