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) = 1-R 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?
Log(T) =ln(T)/ln(10) where Log base 10 and ln base e. T - ln(T)/ln(10) = 1-R T = -W(X) / ln(10) with X = -ln(10)*(10^(R-1)) 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 (Newton-Raphson, 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.