The expression, logp......pppppn radical sign where p≥2,p≤N, when simplified is

dependent on both p & n , Independent of n, but dependent on p

Given , log p ...... p p p p p n radical sign log p P 1 P 1 P 1 P ..... n t i m e s log p p 1 n log p p − n = − n log p p = − n

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The expression, $\log_{p} [\frac{\sqrt[p]{\sqrt[p]{\sqrt[p]{...... \sqrt[p]{p}}}}}{n radical sign}]$ where $p \geq 2, p \leq N,$ when simplified is

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dependent on both p & n

negative

indefinite if p, but dependent on n

Independent of n, but dependent on p

answer is A, D.

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Given , $\log_{p} [\frac{\sqrt[p]{\sqrt[p]{\sqrt[p]{...... \sqrt[p]{p}}}}}{n radical sign}]$

$\log_{p} [{[{[P^{\frac{1}{P}}]}^{\frac{1}{P}}]}^{\frac{1}{P}}] ..... n t i m e s$

$\log_{p} [p^{\frac{1}{n}}]$

$\log_{p} p^{- n}$

$= - n \log_{p} p$

$= - n$

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