\( \log _{10}\left(\log _{2} 3\right)+\log _{10}\left(\log _{3} 4\right)+\log _{10}\left(\log _{...

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\( \log _{10}\left(\log _{2} 3\right)+\log _{10}\left(\log _{3} 4\right)+\log _{10}\left(\log _{4} 5\right)+\ldots \ldots . .+\log _{10}\left(\log _{1023} 1024\right) \) simplifies to
(A) a composite
(B) a prime number
\( \mathrm{P} \)
(C) rational which is not an integer
(D) an integer
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