Question

If ${\log }_{6}x+2{\log }_{36}x+3{\log }_{216}x=9$, then $x=$

• A. 6
• B. 36
• C. 216
• D. None of these

Answer 1

Answer: (C)

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