The value of _2 . _3 .... _ 100 100^ 99 ^ 98 ^ .^ .^ .2 ^1 is - Vidyadip

MCQ

The value of ${\log _2}.{\log _3}....{\log _{100}}{100^{{{99}^{{{98}^{{.^{{.^{{{.2}^1}}}}}}}}}}}$ is

A
$0$
✓
$1$
C
$2$
D
$100!$

✓

Answer

Correct option: B.

$1$

b
(b) ${\log _2}.{\log _3}.....{\log _{99}}$ ${\log _{100}}{100^{{{99}^{{{98}^{{.^{{.^{{.^{{2^1}}}}}}}}}}}}}$

$ = {\log _2}.{\log _3}....{\log _{98}}^{{{98}^{{{97}^{{.^{{.^{{.^{{2^1}}}}}}}}}}}}$

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

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