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Help to figure out equation solution 
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#1
Mar1512, 12:08 AM

P: 6

Hey,
While working on a project I came across an equation and need some help to solve it. This is the equation T  log(T) = 1R Where, T = variable whose value is to be found log base is 10 R = given value so basically right side of equal to sign is a constant.. Can anyone explain how to go about solving for T? 


#2
Mar1512, 03:04 AM

P: 759

Log(T) =ln(T)/ln(10) where Log base 10 and ln base e.
T  ln(T)/ln(10) = 1R T = W(X) / ln(10) with X = ln(10)*(10^(R1)) W(X) is the Lambert W function. If the Lambert W function is not implemented on your maths software, you have to use numerical computation in order to solve the equation (NewtonRaphson, or other methods). The equation has no real solution if R > 1(1+ln(ln(10))/ln(10) = 0.20349 if R=0.20349 there is only one solution T=1/ln(10) = 0.43429 if 0<R<0.20349 there are two real solutions. 


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