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

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In summary, the given equation contains a combination of logarithmic and algebraic terms and cannot be solved using traditional methods. It may require the use of numerical solutions or the Lambert W function.
  • #1
dimensionless
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Homework Statement


Given the equation
[tex]a log_{10}(x)^{2}+b log_{10}(x) + c x + d = 0[/tex]
solve for [tex]x[/tex]

Homework 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

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.
 
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  • #2
I doubt there is an explicit solution for this!
 
  • #3
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.
 

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

Question 1: What is the first step in solving for x in this equation?

The first step in solving for x in this equation is to factor out the common term, log(x), from both the first and second terms.

Question 2: How do you solve for x when there are multiple logarithmic terms in the equation?

To solve for x in this equation, you can use the properties of logarithms to combine the terms into a single logarithmic term. Then, you can solve for x using algebraic techniques.

Question 3: Can this equation have more than one solution for x?

Yes, this equation can have more than one solution for x. In fact, it is possible for there to be an infinite number of solutions depending on the values of a, b, and c.

Question 4: Is it necessary to use logarithmic rules to solve for x in this equation?

Yes, you will need to use logarithmic rules to simplify the equation and solve for x. This is because the equation contains logarithmic terms, and the rules of logarithms allow you to combine and manipulate these terms in order to solve for x.

Question 5: Can this equation be solved without using logarithms?

No, this equation cannot be solved without using logarithms. The presence of logarithmic terms makes it necessary to use logarithmic rules in order to simplify the equation and solve for x.

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