# Express x in terms of the constants

• I

## Main Question or Discussion Point

I have the expression, A(Bx + 1) = C*d^(2x) where A,B,C and d are constants. How to arrive at an expression for x in terms of A,B,C and d?

I have tried doing this:

Log [A(Bx + 1)/C] = Log [d^(2x)]

2xLog(d) = Log[A(Bx + 1)/C]

but I'm unable to arrive at an explicit expression of x in terms of A,B,C and d.

fresh_42
Mentor
This cannot be done, since basically you have a linear term on the left and an infinite sum on the right. The best you can get is by using the Lambert W-function which isn't a function to be exact.

Ssnow
Gold Member
I'm unable to arrive at an explicit expression
because you can't, the best thing you can do is using the Lambert W-function as suggested by @fresh_42 or there is also a graphical method that consist to intersect the linear function ##f(x)\,=\, ABx+A## with the exponential function ##g(x)\,=\,Cd^{2x}##, changing the value of your parameters you can study the existence of solutions of your equation.

Ssnow