Question

if log5log4log3(x²-11x+1)=0 then what is the value of x?

Answer 1

$log_5log_4log_3(x^2-11x+1) = 0 \\ log_4log_3(x^2-11x+1) = 1 \\ log_3(x^2-11x+1)=4 \\ (x^2-11x+1) = 3^4 \\ x^2-11x+1 = 81 \\ x^2-11x-80 =0 \\ x^2-16x+5x-80=0 \\ (x-16)(x+5) =0 \\ x= 16,-5$
but for log to be defined ,
  $x^2-11x+1\ \textgreater \ 0 \\log_4log_3( x^2-11x+1)\ \textgreater \ 0 \\ log_3(x^2-11x+1)\ \textgreater \ 0$
after solving this ,
 x = 16 and -5 both are possible .
  so, x = 16 and -5