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If p,q in N" satisfy the equation "x^(s...

If `p,q in N" satisfy the equation "x^(sqrtx) = (sqrtx)^(x)`, then

A

p+q=5

B

`|p-q|=4`

C

pq=4

D

if ` log_(q) p ` is defined, then ` log_(p)q ` is not and vice versa

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
` x ^(sqrtx)=(sqrtx)^(x) ,p,qinN`
`rArr sqrtx log x = x log sqrtx`
` or log x [sqrtx - x/2] = 0`
` rArr log x = 0 or [sqrtx - x/2] = 0`
` rArr x = 1 or 4`
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