\( \mathrm{P} \) (A) The expression \( \mathrm{x}=\log _{2} \log _{...

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\( \mathrm{P} \)
(A) The expression \( \mathrm{x}=\log _{2} \log _{9} \sqrt{6+\sqrt{6+\sqrt{6+\ldots \ldots \infty}}} \) simplifies to
(P) an integer
(B) The number \( \mathrm{N}=2^{\left(\log _{2} 3 \cdot \log _{3} 4 \cdot \log _{4} 5 \ldots \ldots \ldots . . \cdot \log _{99} 100\right)} \) simplifies to
(Q) a prime
(C) The expression \( \frac{1}{\log _{5} 3}+\frac{1}{\log _{6} 3}-\frac{1}{\log _{10} 3} \) simplifies to
(R) a natural
(D) The number \( \mathrm{N}=\sqrt{2+\sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{14-6 \sqrt{5}}}} \) simplifies to
(S) a composite
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