Question Number 10248 by j.masanja06@gmail.com last updated on 31/Jan/17

solve the value of x     logx^2 =(x/(25))

Answered by mrW1 last updated on 01/Feb/17

I. if x>0:  log x^2 =(x/(25))  ⇒2log x=(x/(25))  log x=(x/(50))  ((ln x)/(ln 10))=(x/(50))  ln x=((ln 10)/(50))x=−ax  with a=−((ln 10)/(50))  ln x=−ax  x=e^(−ax)   xe^(ax) =1  (ax)e^(ax) =a  ⇒ax=W(a)    Lambert W function  ⇒x=((W(a))/a)=−((W(−((ln 10)/(50))))/((ln 10)/(50)))=−((W(−0.046052))/(0.046052))   { ((=((−0.048332)/(−0.046052))=1.049516)),((=((−4.605162)/(−0.046052))=100)) :}    II. if x<0:  log x^2 =(x/(25))  let t=−x, t>0  log (−t)^2 =−(t/(25))  log (t)^2 =−(t/(25))  2log t=−(t/(25))  see above  t=((W(((ln 10)/(50))))/((ln 10)/(50)))  x=−t=−((W(((ln 10)/(50))))/((ln 10)/(50)))=−((W(0.046052))/(0.046052))  =−((0.044067)/(0.046052))=−0.956903    ⇒ x=−((W(±((ln 10)/(50))))/((ln 10)/(50)))≈ { ((−0.956903)),((1.049516)),((100)) :}

Answered by arge last updated on 04/Feb/17

2log x=(x/(25))    log x=y    x=50y