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I Express x in terms of the constants

  1. Nov 26, 2016 #1
    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!
  2. jcsd
  3. Nov 26, 2016 #2


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    Staff: 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.
  4. Nov 27, 2016 #3


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    Gold Member

    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.

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