What is the value of x so that `3^x` is 5 more than `2^2`?

Answer

To find the value of \( x \) such that \( 3^x \) is 5 more than \( 2^2 \), we can follow these steps:

### Step 1: Understand the equation
We start with the statement that \( 3^x \) is 5 more than \( 2^2 \). This can be expressed as:
\[ 3^x = 2^2 + 5 \]

### Step 2: Calculate \( 2^2 \)
Next, we calculate \( 2^2 \):
\[ 2^2 = 4 \]

### Step 3: Substitute \( 2^2 \) into the equation
Now, substitute \( 4 \) back into the equation:
\[ 3^x = 4 + 5 \]

### Step 4: Simplify the right side
Now, we simplify the right side:
\[ 3^x = 9 \]

### Step 5: Express \( 9 \) as a power of \( 3 \)
We know that \( 9 \) can be expressed as:
\[ 9 = 3^2 \]

### Step 6: Set the exponents equal
Since the bases are the same, we can set the exponents equal to each other:
\[ x = 2 \]

### Conclusion
Thus, the value of \( x \) is:
\[ \boxed{2} \]