It seems like you're trying to solve or work with a logarithmic equation, but the expression you provided is a bit unclear. I'll assume you're referring to an equation in the form of:

\[
\log_9(y) = \frac{1}{2}
\]

If this is correct, here's how you can solve it:

### Step-by-Step Solution

1. **Rewrite the logarithmic equation in exponential form**:
   By the definition of logarithms, \(\log_b(a) = c\) is equivalent to \(b^c = a\). So we can rewrite \(\log_9(y) = \frac{1}{2}\) as:

   \[
   9^{\frac{1}{2}} = y
   \]

2. **Simplify the exponential expression**:
   \(9^{\frac{1}{2}}\) is the square root of 9, so:

   \[
   \sqrt{9} = 3
   \]

3. **Conclusion**:
   Therefore, \(y = 3\).

---

Would you like more details on this solution or have any specific questions? Here are five related questions you can explore further:

1. What is the general form of logarithmic and exponential equations?
2. How can logarithms with different bases be converted?
3. What happens when you have \(\log_b(y) = c\) with more complex numbers?
4. How does solving logarithmic equations differ when there is a coefficient in front of \(\log_b(y)\)?
5. Can logarithms be solved graphically?

**Tip**: When solving logarithmic equations, remember that \(\log_b(a) = c\) translates to \(b^c = a\), which helps in converting between logarithmic and exponential forms.

Learn how to solve the logarithmic equation log_9(y) = 1/2 with a detailed step-by-step solution. This problem covers key logarithmic concepts, including converting logarithms to exponential form. Suitable for students in Grades 9-12.

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