Find the product of root of the equation (log3)2-2(log3x)-5=0 .

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Let x1 and x2 be roots of log3x2-2log3x-5=0. So we have to find x1x2Nowlog3x2-2log3x-5=0 ; equationiLet log3x=tlog3x1=t1 and log3x2=t2Now equationi becomes,t2-2t-5=0Its roots are t1 and t2Sum of roots=-Coefficient of tCoefficient of t2 t1+t2=--21log3x1+log3x2=2We know that logam+logan=logamnlog3x1x2=2We know that logax=yx=ayx1x2=32x1x2=9Hence product of roots of the equation  log3x2-2log3x-5=0 is 9.

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