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

Options

A. `0`
B. `3`
C. `5`
D. `2`

Answer

To solve the expression \(2^{\log_{3}5} - 5^{\log_{3}2}\), we will use the property of logarithms that states:

\[ a^{\log_{b}c} = c^{\log_{b}a} \]

### Step 1: Apply the property to the first term

We start with the first term \(2^{\log_{3}5}\). According to the property mentioned, we can rewrite it as:

\[ 2^{\log_{3}5} = 5^{\log_{3}2} \]

### Step 2: Substitute back into the expression

Now we can substitute this back into the original expression:

\[ 2^{\log_{3}5} - 5^{\log_{3}2} = 5^{\log_{3}2} - 5^{\log_{3}2} \]

### Step 3: Simplify the expression

Since both terms are now the same, we can simplify the expression:

\[ 5^{\log_{3}2} - 5^{\log_{3}2} = 0 \]

### Final Answer

Thus, the value of \(2^{\log_{3}5} - 5^{\log_{3}2}\) is:

\[ \boxed{0} \]