https://file.aiquickdraw.com/mathbot/file/17303347089199vy60c9x.jpg

It looks like you've uploaded a set of exponential equations. Let's analyze and solve each equation individually:

1. **Equation 1**: \(\frac{901}{1} = \frac{x \cdot 901}{1 - x \cdot 901}\)
   
   This equation seems to be attempting a form of rational function involving \(x\). To proceed, we'd typically cross-multiply to simplify it.

2. **Equation 2**: \((1 - x) (1 - x e^2) = (81)(1 + x e^2) \cdot x \cdot 6\)

   This equation is quite complex, involving both an exponential term \(e^2\) and multiple products. Expanding and isolating terms involving \(x\) might help to find \(x\).

3. **Equation 3**: \(5 - x \cdot 2 - 0.01 = x \cdot 91\)

   This is a linear equation in \(x\). Combining like terms and isolating \(x\) will provide a solution.

4. **Equation 4**: \(\frac{x \cdot 8}{1} = 13 - x \cdot 5\)

   Another linear equation in \(x\). Simplify by isolating \(x\).

5. **Equation 5**: \(\frac{1}{1 + x \cdot 4} = 64\)

   This can be solved by cross-multiplying and isolating \(x\).

Would you like a detailed solution for each of these equations, or do you have specific questions about one? 

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Here are some related questions to explore:

1. How do you approach solving exponential equations in general?
2. What methods help in simplifying complex rational equations?
3. How can you isolate variables when there are multiple terms on both sides?
4. What does the presence of \(e\) (Euler’s number) suggest about the solution's properties?
5. How can you verify if your solution is correct?

**Tip:** When dealing with multiple equations, solve each individually and simplify as much as possible before trying to interpret or solve them as a system.

Solve the set of equations:
1. (901 / 1) = x (901) / (1 - x * 901)
2. (1 - x)(1 - x e^2) = (81)(1 + x e^2) * x * 6
3. 5 - x * 2 - 0.01 = x * 91
4. x * 8 / 1 = 13 - x * 5
5. 1 / (1 + x * 4) = 64

Learn how to solve a complex set of exponential, linear, and rational equations, involving steps like cross-multiplication and isolating x terms. This solution covers essential concepts for students at an advanced math level.

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