If `a^(2x+2)=1`, where a is a positive real number other than 1, then x = ?

Options

A. -2
B. -1
C. 0
D. 1

Answer

To solve the equation \( a^{2x+2} = 1 \), where \( a \) is a positive real number other than 1, we can follow these steps:

### Step 1: Understand the properties of exponents
Since \( a \) is a positive real number and not equal to 1, we know that \( a^k = 1 \) only when \( k = 0 \). This means we can set the exponent equal to zero.

### Step 2: Set the exponent equal to zero
From the equation \( a^{2x+2} = 1 \), we can conclude:
\[ 2x + 2 = 0 \]

### Step 3: Solve for \( x \)
Now, we will solve the equation \( 2x + 2 = 0 \):
\[ 2x = -2 \]
\[ x = \frac{-2}{2} \]
\[ x = -1 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{-1} \]

---