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$$1.995-505x=(26*10^{-3})*ln(\frac{x}{3*10^{-16}})$$

Apologies for the Title, I couldn't think of a better way to phrase the question.

Anyways, I'm currently working through my microelectronics homework and I've reached a point in my solution in which I am unable to solve for "x" (It's the secondary collector current in a two-transistor circuit, but that's irrelevant.) since there is no way I am aware (Or to be more precise, that I recall.) of to simplify for "x". Since I found a solution manual for my textbook, I know that $x=2.42*10^{-3}$ but it does not state how it reached that value, just how to arrive to the same equation.

So, to reiterate, my question is how one would go about solving this equation for x, besides brute force or putting it into wolfram or like programs. While it would be neat if there was a formula similar such as $Ae^x+Bx+C=0$, I feel as if it's a differential equation, although there's only one variable in this equation, so such a diff-eq would be weird, if not flat out impossible.

As a side-note, if anybody knows any good tags to add to this question, it'd be much appreciated. The only one I can think of is "logarithms".

Edit 1: I mistyped the x= section. Should be 2.42mA

Michael Merrick
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  • i got this here $$0.002420411449$$ – Dr. Sonnhard Graubner Oct 16 '17 at 16:41
  • Thank you, I didn't realize I incorrectly typed the number (put a 3 instead of a 2.). Would you mind explaining how you reached said value? – Michael Merrick Oct 16 '17 at 16:44
  • there is a numerical method, the Newton_Raphson method, also available in the internet – Dr. Sonnhard Graubner Oct 16 '17 at 16:46
  • I'll have to look into it, thank you very much. (While I have not been taught this in a class, I do vaguely recall using this equation to recursively solve square roots in C.) – Michael Merrick Oct 16 '17 at 16:51
  • Alright, thank you for mentioning the Newton-Raphson method. At first I was slightly confused about how you'd find the derivative of f(x), since is wasn't a function, but after some more reading, I learned that f(x) = 0 where f(x) is the entire equation. Edit: Didn't mean to hit enter to post the comment. As a final question, how do I close this question? I don't see an obvious "Close Question" button, or similar. Have a great day! – Michael Merrick Oct 16 '17 at 21:14

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