If `a ^(*)b=2(a+b)` then `5^*2` is equal : to

Options

A. 3
B. 10
C. 14
D. 20

Answer

To solve the problem, we need to evaluate the expression \( 5^*2 \) using the operation defined as \( a^*b = 2(a + b) \).

### Step-by-step Solution:

1. **Identify the operation**: We are given that \( a^*b = 2(a + b) \). This means that for any values of \( a \) and \( b \), we will multiply the sum of \( a \) and \( b \) by 2.

2. **Substitute the values**: We need to find \( 5^*2 \). According to the operation defined, we substitute \( a = 5 \) and \( b = 2 \):
\[ 5^*2 = 2(5 + 2) \]

3. **Calculate the sum**: First, we calculate the sum inside the parentheses:
\[ 5 + 2 = 7 \]

4. **Multiply by 2**: Now, we multiply the result by 2:
\[ 2 \times 7 = 14 \]

5. **Final result**: Therefore, \( 5^*2 = 14 \).

### Conclusion:
The value of \( 5^*2 \) is \( 14 \).