How Do You Solve This Complex Exponential Equation for x?

• adc85
In summary, the conversation discusses a problem with solving for x in a transcendental equation. The speaker attempted to solve it using a graphical method but was unsuccessful. They also share their frustration with Calculus-Based Statistics and advise against taking it unless necessary for one's major.
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.

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.

1. How do I approach solving this equation?

When faced with a difficult equation, it's important to first simplify and identify any patterns or relationships within the equation. Then, try to isolate the variable on one side of the equation by using inverse operations. Finally, check your answer by plugging it back into the original equation.

2. What if I'm stuck and can't seem to make any progress?

If you're feeling stuck, try breaking down the equation into smaller parts and solving them one at a time. You can also try using different methods or strategies, such as substitution or factoring, to approach the problem from a different angle.

3. Do I need to solve the equation algebraically or can I use a calculator?

It depends on the specific equation and the instructions given. In some cases, using a calculator may be acceptable, but it's important to show your work and explain your thought process in your solution.

4. Can I check my answer to make sure it's correct?

Yes, it's always a good idea to check your answer by plugging it back into the original equation and making sure it satisfies the given equation. It's also helpful to double check your calculations to avoid any simple mistakes.

5. Are there any common mistakes to watch out for when solving equations?

Yes, some common mistakes include forgetting to distribute properly, not following the order of operations, and making errors in simplifying fractions or solving for negative numbers. It's important to pay attention to detail and check your work carefully.

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