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 can use the property of logarithms that states:

\[ a^{\log_b{c}} = c^{\log_b{a}} \]

### Step 1: Rewrite \(2^{\log_3{5}}\)

Using the logarithmic property mentioned above, we can rewrite \(2^{\log_3{5}}\):

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

### 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 we have \(5^{\log_3{2}} - 5^{\log_3{2}}\), this simplifies to:

\[ 0 \]

### Conclusion

Thus, the value of \(2^{\log_3{5}} - 5^{\log_3{2}}\) is:

\[ \boxed{0} \]

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