- #1

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I was solving an engineering problem and I got to the form

[tex]ax=b-cln(dx)[/tex]

where a, b, c and d are constant real values. I had a peek at the answer and they got a unique positive real valued answer for x but I have no idea how. Some searching I came across the Lambert W-Function and I got it into the form

[tex]\frac{1}{d}e^{\frac{b}{c}} = xe^{\frac{ax}{c}} [/tex]

How do I proceed to apply the Lambert W-Function from here?

WolframAlpha found that

[tex]x = \frac{c}{a}W\left ( \frac{a}{cd}e^{\frac{b}{c}} \right )[/tex]