The value of `2^("log"3^(5)) - 5^("log"3^(2))` is

Options

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

Explanation

To solve the expression \( 2^{\log_3(5)} - 5^{\log_3(2)} \), we will use the properties of logarithms and exponents.

### Step-by-Step Solution:

1. **Apply the Change of Base Formula**:
We know that \( a^{\log_b(c)} = c^{\log_b(a)} \). We can apply this property to both terms in our expression.

\[ 2^{\log_3(5)} = 5^{\log_3(2)} \]

Thus, we can rewrite the expression:

\[ 2^{\log_3(5)} - 5^{\log_3(2)} = 5^{\log_3(2)} - 5^{\log_3(2)} \]

2. **Simplify the Expression**:
Now that we have both terms equal, we can simplify:

\[ 5^{\log_3(2)} - 5^{\log_3(2)} = 0 \]

### Final Answer:
The value of \( 2^{\log_3(5)} - 5^{\log_3(2)} \) is \( 0 \).