SOLUTION: A = ln(x)-Bx Express x in terms of A and B. Please help.... thanks in advance.....

Question 433406: A = ln(x)-Bx
Express x in terms of A and B.
Please help.... thanks in advance.....
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!

Multiply both sides by -B

There is a certain function called the Lambert W-function defined as the inverse of the function . Here, we have so it follows that if we take the W-function of both sides,

This is pretty much the simplest form that one can express x in, even though the W-function is somewhat obscure. There is, of course, using Newton's method, but it is very unlikely that a real number will be obtained.

Also, I checked my answer on Wolfram Alpha by putting arbitrary values for A and B (e.g. A = 253, B = 19), and it came out with the solution .

http://www.wolframalpha.com/input/?i=253+%3D+ln%28x%29+-+19x

Wikipedia article about the W-function:
http://en.wikipedia.org/wiki/Lambert_W_function

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