How Do You Solve This Complex Exponential Equation for x?

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The discussion focuses on solving the complex exponential equation (e^10-11)^-1*(-e^(10-x)-e^10-x) = p for the variable x. Participants conclude that this equation is transcendental and cannot be explicitly solved for x using analytical methods. The recommended approach is to utilize graphical methods to find potential intersection points between the two sides of the equation. One user, Daniel, confirms that after graphing both sides, no intersections were found, indicating that the Cumulative Distribution Function (CDF) may be incorrect.

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Trying to solve for x here...

(e^10-11)^-1*(-e^(10-x)-e^10-x) = p

So I try:

(-e^(10-x)-e^10-x) = (e^10-11)p
e^(10-x) = -(e^10-11)p-e^10-x
ln(e^(10-x)) = ln(-(e^10-11)p-e^10-x)
10-x = ln(-(e^10-11)p-e^10-x)

I get stuck there and don't know what to do. Any help appreciated.
 
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I don't think this can be explicitly solved for x.
 
Typically a transcendental equation, no analytical methods to find a solution, if any. Best method, either find it through a graphical method (plot 2 graphs and the solution to your problem is/are the intersection point(s), if any.

Daniel.
 
I graphed the left side of the equation and then graphed the other side (p being X). They do not intersect anywhere. Guess my CDF (Cumulative Distribution Function) is wrong.

Ug and to think I got straight A's in all other Math courses so far. This one is just ridiculous. Never take Calculus-Based Statistics unless you have to for your major.
 

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