What math do I need to solve this: 0.5x^2 - 2x + lnx = -1.687?

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In summary, the conversation discusses the difficulty of solving a type of equation without using numerical means. The use of the Lambert-W function is mentioned as a possible solution. The conversation also brings up the idea of using limit processes to find a solution. Ultimately, an approximation of the solution is found through graphing and using numerical tools.
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tmoney120
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TL;DR Summary
How do you solve an equation that has both a quadtratic and logarithmic term?
I am looking for information on this type of equation but I don't know the terminology so I could not find anything for these types of equations:

0.5x^2 -2x + lnx = -1.687

What math do I need to solve something like this algebraically?
 
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  • #2
Such things are not really solvable algebraically. I.e. you won't be able to get an answer in terms of standard functions.

You might be able to express in answer in terms of the Lambert-W function though. See https://en.wikipedia.org/wiki/Lambert_W_function
 
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  • #3
You won't get a nice algebraic solution. Even for a much simpler case, x+ln(x)=c there is no such thing (with exceptions, of course). There are solutions with functions that basically say "f(x) is the solution. Here is your solution: f(x)" and there might be solutions that involve some limit processes.
 
  • #4
Thanks! I thought so, but wanted to see if I missed something obvious, maybe complex numbers or something, but anyway, thanks and see you around the forums!

The answer is 0.351 by the way, and I got that by graphing the function.
 
  • #5
tmoney120 said:
The answer is 0.351 by the way, and I got that by graphing the function.
No, that's an approximation to the answer. The other people responding to your question said that the problem isn't solvable algebraically (except possibly by the Lambert W function), but one can use numerical means, including looking at a graph, to get a reasonably close approximation.
Wolframalpha gives the solution as .351307, which is again an approximation, and not the exact solution.
 
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1. What is the purpose of using math to solve this equation?

The purpose of using math to solve this equation is to find the value(s) of x that make the equation true. This is important in many scientific and real-world applications, as it allows us to make predictions and solve problems.

2. Do I need to know any specific math concepts to solve this equation?

Yes, you will need to have a basic understanding of algebra and calculus. Specifically, you will need to know how to solve quadratic equations, work with logarithms, and manipulate equations using algebraic rules.

3. Can I use a calculator to solve this equation?

Yes, you can use a calculator to solve this equation. However, it is important to have a good understanding of the underlying concepts and steps involved in solving the equation, as blindly using a calculator can lead to errors.

4. What is the most challenging part of solving this equation?

The most challenging part of solving this equation is likely to be manipulating the equation algebraically to isolate the variable x. This may involve using multiple steps and techniques, and can be especially challenging if you are not familiar with the underlying concepts.

5. Are there any tips or tricks for solving this equation?

One tip for solving this equation is to start by simplifying the equation as much as possible before attempting to solve it. This may involve combining like terms, factoring, or using logarithm rules. Another helpful strategy is to check your answer(s) by plugging them back into the original equation to ensure they make the equation true.

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