The Given equation is (Log3 x)(Log9x) =8
Now change the base 9 to base 3 in Log 9 x.
Log9x = (Log3x)/ (Log39)
= ½ Log3 x [Log39= Log3 32 = 2 Log33 = 2]
The Equation thus becomes
½ (Log3 x)2 = 8
Or, (Log3x)2 = 16
Log3x = 4
Or x = 34
=81
Ans
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