# Solving for x: a*log(x)+b*log(x)^2+c*x = 0

1. Feb 7, 2008

### dimensionless

1. The problem statement, all variables and given/known data
Given the equation
$$a log_{10}(x)^{2}+b log_{10}(x) + c x + d = 0$$
solve for $$x$$

2. Relevant equations
I don't think the quadratic equation will work here. There are a lot of equations at these two pages:

http://en.wikipedia.org/wiki/Logarithm
http://en.wikipedia.org/wiki/Logarithmic_identity

3. The attempt at a solution

I'm not sure where to start. I'm not sure that it is possible to solve. If it is possible, and it hasn't been solved before, then it might take some serious hacking.

2. Feb 7, 2008

### sutupidmath

I doubt there is an explicit solution for this!

3. Feb 7, 2008

### HallsofIvy

Staff Emeritus
Because of the x both within and outside the logarithm, you won't be able find a simple "algebraic" expression for for x. You might use numerical solution or the Lambert W function.