https://file.aiquickdraw.com/mathbot/file/1727227993829ttkqo843.jpg

The equation in the image is:

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

To solve for \( x \), we can follow these steps:

### Step 1: Express both sides in terms of base 5
We can rewrite \( 25 \) and \( \sqrt{5} \) as powers of 5:
\[
25 = 5^2 \quad \text{and} \quad \sqrt{5} = 5^{1/2}
\]

Thus, the right-hand side becomes:
\[
25 \sqrt{5} = 5^2 \times 5^{1/2} = 5^{2 + 1/2} = 5^{5/2}
\]

### Step 2: Equate the exponents
Now the equation becomes:
\[
5^{x - 1} = 5^{5/2}
\]

Since the bases are the same, we can set the exponents equal to each other:
\[
x - 1 = \frac{5}{2}
\]

### Step 3: Solve for \( x \)
Add 1 to both sides:
\[
x = \frac{5}{2} + 1 = \frac{5}{2} + \frac{2}{2} = \frac{7}{2}
\]

Thus, the solution is:
\[
x = \frac{7}{2}
\]

Would you like more details or have any other questions?

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Here are 5 related questions you can explore:
1. What is the general solution to an exponential equation?
2. How do we handle fractional exponents in equations?
3. What is the relationship between square roots and exponents?
4. How can we express different powers of the same base?
5. How do we apply logarithms to solve exponential equations?

**Tip**: Always look to express terms with the same base when solving exponential equations.

Nilai x yang memenuhi 5^(x - 1) = 25√5 adalah...

Find the value of x that satisfies the equation 5^(x - 1) = 25√5 with a detailed step-by-step solution. Learn about exponent rules, expressing terms with the same base, and solving exponential equations. Suitable for high school students in Grades 10-12.

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