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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