I have to solve this
$$ x+a^x=b$$ for $x$?
I know that I have to use logarithms to extract $x$.
But I someohow I have to get rid of the summand $x$ or get it into an exponent.
So how would I go about solving this Equation?
How do I solve this Equation: $x+a^x=b$
0
$\begingroup$
logarithms
exponential-function
-
1I'm afraid that you'll need to deal with the Lambert-W function. So the short answer would be that you cannot express "simply" the solution. – 2017-02-14
-
0Then i probably solved the execrcise wrong, heres the full expression, which I need to solve for h: p(h)=q*e^(-h/H) – 2017-02-14
-
0Mmmm not knowing the function $p(h)$ I can't guarantee that the result would help you but : $$ p(h) = q\cdot e^{-h/H} \implies \ln(p(h)) = \ln(q) -h/H \implies H\cdot (\ln(q) - \ln(p(h))) = h $$ – 2017-02-14
-
0p(h just means p*h). the problem is how to get the h out – 2017-02-14
-
0Then I'm afraid that my first claim was right : [Result](https://tinyurl.com/juqr773). – 2017-02-14