Solve for x :
`(49)^(x + 4) = 7^(2) xx (343)^(x + 1)`

Answer

To solve the equation \( (49)^{(x + 4)} = 7^{2} \times (343)^{(x + 1)} \), we can follow these steps:

### Step 1: Rewrite the bases
We know that \( 49 = 7^2 \) and \( 343 = 7^3 \). Therefore, we can rewrite the equation as:
\[ (7^2)^{(x + 4)} = 7^{2} \times (7^3)^{(x + 1)} \]

### Step 2: Apply the power of a power property
Using the property \( (a^m)^n = a^{m \cdot n} \), we can simplify the left side:
\[ 7^{2(x + 4)} = 7^{2} \times 7^{3(x + 1)} \]

### Step 3: Simplify the right side
Using the property \( a^m \times a^n = a^{m+n} \), we can combine the terms on the right:
\[ 7^{2(x + 4)} = 7^{2 + 3(x + 1)} \]

### Step 4: Set the exponents equal
Since the bases are the same, we can set the exponents equal to each other:
\[ 2(x + 4) = 2 + 3(x + 1) \]

### Step 5: Expand both sides
Expanding both sides gives:
\[ 2x + 8 = 2 + 3x + 3 \]

### Step 6: Combine like terms
This simplifies to:
\[ 2x + 8 = 5 + 3x \]

### Step 7: Rearrange the equation
Now, let's move all terms involving \( x \) to one side and constant terms to the other side:
\[ 2x - 3x = 5 - 8 \]
This simplifies to:
\[ -x = -3 \]

### Step 8: Solve for \( x \)
Multiplying both sides by -1 gives:
\[ x = 3 \]

### Final Answer
The solution for \( x \) is:
\[ \boxed{3} \]