How Do I Solve a Logarithmic Equation with Parameters and Find the Value of x?

In summary, the conversation is about finding the value of x in the equation a*x + b*ln(x) = c, with parameters a, b, and c. The person asks if they need to use differential equations and another person suggests using the Newton Raphson method. They also mention using a scientific calculator or Excel to compute the result. Another person brings up the Lambert's W function as a possible solution.
  • #1
abra
2
0
Hi everyone. I'm new in the forum and I'd need an help to solve this equation (sorry, I think it's quite easy but I'm not an expert of mathematics..):

a*x + b*ln(x) = c

where a, b, c are parameters and I need to find the value of x.

Do I need to use techniques of differential equations?

Thanks a lot for any help.
 
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  • #2
You need to use Numerical Techniques.
Have u come across Newton Raphson method ? It should do just fine on this one.

-- AI
 
  • #3
No, I've never used the Newton Raphson method.. thanks, i'll have a look to this technique, however, I suppose I need to use some maths softwares to compute the result, isn't it?
 
  • #4
No. Any scientific calculator will work. You could also use Excel, if you choose.

Hopefully, you won't have to go through too many iterations.
 
  • #5
There is also the "Lambert's W" function. It is defined specifically as "W(x) is the y satisfying yey= x". In other words, it is the inverse of the function xex.
 

Related to How Do I Solve a Logarithmic Equation with Parameters and Find the Value of x?

1. What is a logarithmic equation?

A logarithmic equation is an equation that contains a logarithm, which is the inverse of an exponential function. It is typically written in the form y = logb(x), where b is the base of the logarithm.

2. How do I solve a logarithmic equation?

To solve a logarithmic equation, you can use the properties of logarithms such as the product rule, quotient rule, and power rule. You can also convert the logarithmic equation into an exponential form and solve for the variable.

3. What are the applications of logarithmic equations?

Logarithmic equations are commonly used in fields such as science, engineering, and finance. They can be used to model exponential growth or decay, calculate pH levels, and solve various real-world problems involving exponential relationships.

4. How do I know when to use a logarithmic equation?

You can use a logarithmic equation when you want to solve for the exponent in an exponential relationship. For example, if you know the base and the result of an exponential function, you can use a logarithmic equation to find the exponent.

5. Can logarithmic equations have negative solutions?

Yes, logarithmic equations can have negative solutions. This can happen when the base of the logarithm is a number between 0 and 1, as the logarithm of a number between 0 and 1 is a negative number. It is important to check the domain of the logarithmic equation to ensure that the solution is valid.

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