a*x=ln{(x-b)/(x+b)}
a and b are constants.
Any help or idea to solve the equation.
Hello EmillyYou'll have to use a numerical method or something like a spreadsheet to solve this equation, and it will only have a solution for certain values of and .
I attach a graph I produced in Excel, to show the result when and . For these values, the equation has the approximate solution , which I found this value using Excel's 'Goal Seek'. There is also another branch of the log graph for values of less than , which I haven't included in the diagram.
You'll see that there are no points on the log graph where , and as , the graph from below. So there won't be any solution if for positive values of .
I'll leave you to work out what will happen to the graphs for different values of and .
Grandad
Hello EmillyDo you know Newton's method (also known as Newton-Raphson) for the approximate solution of equations?
Ifthen
Newton's method gives you an algorithm to find successive approximations to a root of the equation. If is the approximation, then the next is given by:
But if all you need is a numerical answer to a particular equation, then it's much quicker to use a 'Goal Seek' method in a spreadsheet.
Grandad