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  4. If log 6 x+2 log 36 x+3 log 216 x=9, then x=

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Q. If $\log _6 x+2 \log _{36} x+3 \log _{216} x=9$, then $x=$

Logarithms

Solution:

$\log _6 x+2 \log _{36} x+3 \log _{216} x=9 $
$\Rightarrow \log _6 x+\log _6 x+\log _6 x=9 $
$\Rightarrow 3 \log _6 x=9 \Rightarrow \log _6 x=3$
$\Rightarrow x=6^3 $
$\therefore x=216 .$