How Do You Solve This Complex Exponential Equation for x?

[adc85]

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.

 

[TD]

I don't think this can be explicitly solved for x.

 

[dextercioby]

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.

 

[adc85]

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.