Question

( 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 )

# 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.

Solution