Solve for x :
`9^(x + 2)) = 720 + 9^(x)`

Answer

To solve the equation \( 9^{(x + 2)} = 720 + 9^x \), we can follow these steps:

### Step 1: Rewrite the left-hand side
Using the property of exponents, we can rewrite \( 9^{(x + 2)} \) as \( 9^2 \cdot 9^x \):
\[ 9^{(x + 2)} = 9^2 \cdot 9^x \]
So the equation becomes:
\[ 9^2 \cdot 9^x = 720 + 9^x \]

### Step 2: Substitute \( 9^2 \)
Since \( 9^2 = 81 \), we can substitute this into the equation:
\[ 81 \cdot 9^x = 720 + 9^x \]

### Step 3: Rearrange the equation
Next, we can rearrange the equation to isolate terms involving \( 9^x \):
\[ 81 \cdot 9^x - 9^x = 720 \]
Factoring out \( 9^x \) gives us:
\[ (81 - 1) \cdot 9^x = 720 \]
This simplifies to:
\[ 80 \cdot 9^x = 720 \]

### Step 4: Solve for \( 9^x \)
Now, divide both sides by 80:
\[ 9^x = \frac{720}{80} \]
Calculating the right-hand side:
\[ 9^x = 9 \]

### Step 5: Solve for \( x \)
Since \( 9^x = 9 \), we can express 9 as \( 9^1 \):
\[ 9^x = 9^1 \]
Since the bases are the same, we can equate the exponents:
\[ x = 1 \]

### Final Answer
Thus, the solution for \( x \) is:
\[ \boxed{1} \]