https://file.aiquickdraw.com/mathbot/file/1727061634808yqdf5q6w.jpg

The equation provided in the image is:

\[
5^{5x-1} = \sqrt{25^{3x}}
\]

We will solve for \( x \) step-by-step.

### Step 1: Simplify the right-hand side
The square root can be written as an exponent of \( \frac{1}{2} \). So:

\[
\sqrt{25^{3x}} = (25^{3x})^{\frac{1}{2}} = 25^{\frac{3x}{2}}
\]

Also, note that \( 25 = 5^2 \). Therefore:

\[
25^{\frac{3x}{2}} = (5^2)^{\frac{3x}{2}} = 5^{3x}
\]

Now the equation becomes:

\[
5^{5x-1} = 5^{3x}
\]

### Step 2: Equate the exponents
Since the bases are the same (both are powers of 5), we can set the exponents equal to each other:

\[
5x - 1 = 3x
\]

### Step 3: Solve for \( x \)
Now, subtract \( 3x \) from both sides:

\[
5x - 3x = 1
\]

\[
2x = 1
\]

\[
x = \frac{1}{2}
\]

Thus, the value of \( x \) is \( \frac{1}{2} \).

### Answer:
The correct answer is **C. \( \frac{1}{2} \)**.

---

Do you want further details on the solution process or have any other questions?

Here are 5 related questions for you:
1. What are the properties of exponents that were used in this solution?
2. How do we simplify an equation when both sides have the same base?
3. What is the general form of solving logarithmic equations involving exponents?
4. How does the square root function relate to exponentiation?
5. What happens if we change the base in an equation like this?

**Tip:** When dealing with equations involving exponents, always check if you can rewrite both sides to have the same base—it simplifies the solution dramatically!

Nilai x dari bentuk 5^(5x-1) = √(25^(3x)) adalah .... A. -2 B. -1/2 C. 1/2 D. 1/3 E. 1

Learn how to solve the equation 5^(5x-1) = √(25^(3x)) step-by-step. This problem involves algebraic manipulation of exponents and square roots, using exponent properties to find x. Suitable for students in Grades 10-12.

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