Find the value of `3^(2log_(9)3)`.

Explanation

To solve the problem \( 3^{2 \log_{9} 3} \), we can follow these steps:

### Step 1: Rewrite the logarithm
We start with the expression:
\[ y = 3^{2 \log_{9} 3} \]
Using the change of base formula for logarithms, we can rewrite \( \log_{9} 3 \) as:
\[ \log_{9} 3 = \frac{\log_{3} 3}{\log_{3} 9} \]
Since \( \log_{3} 3 = 1 \) and \( \log_{3} 9 = \log_{3} (3^2) = 2 \log_{3} 3 = 2 \), we have:
\[ \log_{9} 3 = \frac{1}{2} \]

### Step 2: Substitute back into the expression
Now we can substitute \( \log_{9} 3 \) back into the expression for \( y \):
\[ y = 3^{2 \cdot \frac{1}{2}} \]

### Step 3: Simplify the exponent
This simplifies to:
\[ y = 3^{1} \]

### Step 4: Calculate the final value
Thus, we find:
\[ y = 3 \]

### Final Answer
The value of \( 3^{2 \log_{9} 3} \) is \( 3 \).

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