The value of $l o g_{2} l o g_{3} . . . . l o g_{100}^{100^{99^{98^{⋮^{2^{1}}}}}}$

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Solution

The correct option is B 1
$l o g_{2} . l o g_{3} . . . . l o g_{99} l o g_{100} 100^{99^{98^{⋮^{2^{1}}}}} = l o g_{2} l o g_{3} . . . . l o g_{99} 99^{98^{⋮^{2^{1}}}} [l o g_{100} 100 = 1] S i m i l a r l y, l o g_{2} l o g_{3} . . . . l o g_{98} 98^{97^{⋮^{2^{1}}}} = l o g_{2} l o g_{3} . . . . l o g_{97} 97^{96^{⋮^{2^{1}}}} = l o g_{2} l o g_{3} 3^{2^{1}} = l o g_{2} 2^{1} l o g_{3} 3 = l o g_{2} 2 = 1.$

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