https://file.aiquickdraw.com/mathbot/file/1726879828741pcgik07r.jpg

The equation provided in the image is:

\[
5^x = 25 \sqrt{5}
\]

### Steps to solve the equation:

1. Express both sides of the equation in terms of powers of 5. We know that:
   \[
   25 = 5^2 \quad \text{and} \quad \sqrt{5} = 5^{1/2}
   \]
   Thus, the right-hand side becomes:
   \[
   25 \sqrt{5} = 5^2 \cdot 5^{1/2} = 5^{2 + 1/2} = 5^{5/2}
   \]

2. Now, the equation becomes:
   \[
   5^x = 5^{5/2}
   \]

3. Since the bases are the same, we can set the exponents equal to each other:
   \[
   x = \frac{5}{2}
   \]

### Therefore, the value of \( x \) is \( \frac{5}{2} \) or 2.5.

Let me know if you'd like further clarification or a different approach to this problem. Here are a few related questions to consider:

1. How do we handle exponents with fractions in different types of equations?
2. What are other methods of solving exponential equations with the same base?
3. Can we solve similar equations where the base isn't a perfect power (like 5)?
4. What is the role of logarithms in solving exponential equations?
5. How can we graphically represent the equation \( 5^x = 25\sqrt{5} \)?

**Tip:** Always try to express terms in exponential form when solving exponential equations—it makes the solution more straightforward!

Nilai x yang memenuhi 5^x = 25√5 adalah ....

Learn how to solve the exponential equation 5^x = 25√5 step by step, by expressing terms in exponential form and applying the laws of exponents. Suitable for students in Grades 10-12.

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