To solve the equation \(9^x + 15^x = 25^x\), let's follow these steps:

### Step 1: Simplify the bases
We can express the numbers \(9\), \(15\), and \(25\) as powers of smaller numbers:
- \(9 = 3^2\)
- \(15 = 3 \cdot 5\)
- \(25 = 5^2\)

Thus, the equation becomes:
\[
(3^2)^x + (3 \cdot 5)^x = (5^2)^x
\]
This simplifies to:
\[
3^{2x} + (3^x \cdot 5^x) = 5^{2x}
\]

### Step 2: Test for simple solutions
Let's check for simple values of \(x\) to see if we can find any integer solutions.

#### Case 1: \(x = 1\)
Substitute \(x = 1\) into the original equation:
\[
9^1 + 15^1 = 25^1
\]
\[
9 + 15 = 25
\]
\[
24 = 25
\]
This is false, so \(x = 1\) is not a solution.

#### Case 2: \(x = 2\)
Substitute \(x = 2\) into the original equation:
\[
9^2 + 15^2 = 25^2
\]
\[
81 + 225 = 625
\]
\[
306 \neq 625
\]
This is also false, so \(x = 2\) is not a solution.

### Step 3: Consider other methods
The equation does not seem to have simple integer solutions. We might consider more advanced methods, such as logarithms or numerical approximations, to solve for \(x\).

Alternatively, the equation can also be solved numerically using graphing techniques or numerical solvers.

### Final Conclusion:
After testing some simple values of \(x\), it appears that there are no easy integer solutions. Solving this equation would require numerical methods, and based on graphing or numerical computation, we may be able to find the exact value of \(x\).

Would you like to proceed with a numerical approximation or a graph of the equation to find the solution?

### Related Questions:
1. What methods can be used to solve exponential equations?
2. How do logarithmic transformations help solve equations with exponents?
3. How does numerical approximation work for solving non-linear equations?
4. What is the process of solving equations graphically?
5. What are some common applications of exponential equations in real life?

### Tip:
Always test for simple integer solutions first when dealing with exponential equations—this can save time and offer quick insights.

Explore how to solve the equation 9^x + 15^x = 25^x with detailed steps and methods including exponential equations, logarithms, and numerical methods. This problem challenges advanced high school students and beyond.

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