I Express x in terms of the constants

[vktsn0303]

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.
Can someone please help?

Thanks in advance!

 

[fresh_42]

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]

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