Question

Find the value of ${\log }_2.{\log }_3.........{\log }_{100}.100.99.98..............2.1$

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Answer 1

${\log }_2.{\log }_3.........{\log }_{100}.100.99.98..............2.1$

We know ${\log }_{100}$ 100 = 1

So, ${\log }_2.{\log }_3.........{\log }_{99}.99.98..............2.1$ {${\log }_{100}100$}

{${\log }_{a}a=1$}

= ${\log }_2.{\log }_3.........{\log }_{98}.98.97..............2.1$ {${\log }_{99}99$}

If we keep on doing process

We will be getting

${\log }_2.{\log }_3{3}^{2^1}$ = ${\log }_2{2}^1$ = 1