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10^(logp(logq(logr(x))))=1 and logq(logr...

`10^(log_p(log_q(log_r(x))))=1` and `log_q(log_r(log_p(x)))=0` then 'p' equals

A

`r^(q//r)`

B

rq

C

1

D

`r^(r//q)`

Text Solution

Verified by Experts

The correct Answer is:
A
`10^(log_(p)(log_(q)(log_(r )x)))=1`
`rArr log_(p)(log_(q)(log_(r )x))=0`
`rArr log_(q)(log_(r )x)=1`
`therefore log_(r )x=q`
`rArr x=r^(q)`
`log_(q)(log_(r )(log_(p)x)=0`
`rArr log_(r )(log_(p)x)=1`
`rArr log_(p)x=r`
`rArr x=p^(r )`
From (1) and (2), `r^(q)=p^(r )`
`rArr p=r^(q//r)`
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