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