The value of `2^("log"_(3)7) - 7^("log"_(3)2)` is

Options

A. `"log"2`
B. 1
C. 0
D. none of these

Answer

To solve the expression \(2^{\log_3 7} - 7^{\log_3 2}\), we can use the property of logarithms that states \(a^{\log_b c} = c^{\log_b a}\).

### Step-by-Step Solution:

1. **Identify the expression**:
We start with the expression:
\[ 2^{\log_3 7} - 7^{\log_3 2} \]

2. **Apply the logarithmic property**:
Using the property \(a^{\log_b c} = c^{\log_b a}\), we can rewrite \(2^{\log_3 7}\):
\[ 2^{\log_3 7} = 7^{\log_3 2} \]
Thus, we can replace \(2^{\log_3 7}\) in our original expression:
\[ 2^{\log_3 7} - 7^{\log_3 2} = 7^{\log_3 2} - 7^{\log_3 2} \]

3. **Simplify the expression**:
Since both terms are identical, we have:
\[ 7^{\log_3 2} - 7^{\log_3 2} = 0 \]

4. **Conclusion**:
Therefore, the value of the expression is:
\[ \boxed{0} \]