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log3 log2 logsqrt3 (81) = ....

`log_3 log_2 log_sqrt3 (81)` = ______.

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Evaluate log_2 log_2 log_3 81

Which of the following when simplified reduces to unity? I. log_(1.5) log_(4) log_sqrt3 81 II. log_(2) sqrt6 +log_(2) sqrt(2/3) III. -1/6log_(sqrt(3)/2) ((64)/(27)) IV. log_(3.5) (1+2+3/6) The correct choice is:

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If P =3^sqrt(log_(3)2)-2^(sqrt(log_(2)3))and Q=log_(2)log_(3)log_(2)log _(sqrt(3))81, then

log_(2)[log_(2) {log_(2)(log_(3) 81)}] =