3. Find the square of the sum of th...
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3. Find the square of the sum of the roots of the equation log.x.log.x.log,x = log x.log.x + log.x.logsx + log,x.log,x.

JEE/Engineering Exams
Maths
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( log _{3} x log _{4} x log _{3} x=log _{3} x log _{4} x+log _{4} x log _{5} x+log _{5} x cdot log _{3} x ) ( Rightarrow frac{(log x)^{3}}{log 3 lg 4 lg 5}=frac{(log 5)(log x)^{2}+(lg 3)^{3}(log x)^{2}+left(log _{4}right)(log x)^{2}}{log 3 log 4 log } ) a) ( (log x)^{3}=(lg x)^{2}(log 5+log 3+log 4) ) 9) ( (log x)^{3}-(log x)^{2}(log 60)=0 ) ( Rightarrow quad(log x)^{2}(log x-log 60)=0 ) o) ( log x=0 quad ) or ( quad log x=log 60 ) ( Rightarrow quad x=1 quad ) OR ( quad x=60 ) Rosts are 1 and 60 . Squar of sum of rosts ( =1+3600 ) ( =3601 )
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