How do I calculate the value of a predictor variable in logistic and exponential equations?

Question

I need some help on some algebra in order to retrieve a predictor value for a given value of the response variable. How to I solve for ψ (predictor) given these values of ε (response) from the following equations? If you could show workings that would be great. Thanks so much!

Logistic equation 1: 355 = 355/ (1 + exp^{(-((ψ-1.47)/0.70))})

Logistic equation 2: 54.5 = 54.5/ (1 + ((ψ/7.41)^1.70))

Exponential equation 1: 1015 = 424 + 4681exp^(-3.9*ψ)

Answer 1

Alan,

The answer to 1. is Ψ→∞ #2 by inspection

The answer to #2 is Ψ=0 again by inspection

The answer to #3 is :

1015=424+468e^-3.9x simplify this equation to 591=568e^-3.9x then ln(1.262)=-3.9x

so x=-.05983 approx.

Regards

Jim