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  4. If log 4 log 3 log 2 x vanishes, then the characteristic of the logarithm of 1000 to the base x, is

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Q. If $\log _4 \log _3 \log _2 x$ vanishes, then the characteristic of the logarithm of 1000 to the base $x$, is

Continuity and Differentiability

Solution:

$x =8 \Rightarrow \log _8 1000=\log _2 10$
$\therefore$ Characteristic is 3.