Find the value of x, if `(3^(2x-2) + 54) div 15 = 9.`

Options

A. 5
B. 7
C. 3
D. 4

Answer

To solve the equation \((3^{(2x-2)} + 54) \div 15 = 9\), we will follow these steps:

### Step 1: Eliminate the division
Multiply both sides of the equation by 15 to eliminate the division:

\[ 3^{(2x-2)} + 54 = 9 \times 15 \]

### Step 2: Calculate the right side
Calculate \(9 \times 15\):

\[ 3^{(2x-2)} + 54 = 135 \]

### Step 3: Isolate the exponential term
Subtract 54 from both sides to isolate the exponential term:

\[ 3^{(2x-2)} = 135 - 54 \]

### Step 4: Calculate the right side
Calculate \(135 - 54\):

\[ 3^{(2x-2)} = 81 \]

### Step 5: Express 81 as a power of 3
Recognize that \(81\) can be expressed as \(3^4\):

\[ 3^{(2x-2)} = 3^4 \]

### Step 6: Set the exponents equal to each other
Since the bases are the same, we can set the exponents equal to each other:

\[ 2x - 2 = 4 \]

### Step 7: Solve for \(x\)
Add 2 to both sides:

\[ 2x = 4 + 2 \]

\[ 2x = 6 \]

Now divide by 2:

\[ x = 3 \]

### Final Answer
Thus, the value of \(x\) is:

\[ \boxed{3} \]

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