The value of `(2^(log_(3)7)-7^(log_3 2))` is :

Options

A. 0
B. 1
C. `log_(7)5`
D. `log_(7)6`

Answer

To solve the expression \(2^{\log_{3} 7} - 7^{\log_{3} 2}\), we can use the properties of logarithms. Here’s a step-by-step solution:

### Step 1: Identify the expression
We start with the expression:
\[ 2^{\log_{3} 7} - 7^{\log_{3} 2} \]

### Step 2: Apply the logarithmic identity
We can use the property of logarithms that states:
\[ a^{\log_{b} c} = c^{\log_{b} a} \]
This means we can rewrite \(7^{\log_{3} 2}\) as \(2^{\log_{3} 7}\).

### Step 3: Rewrite the expression
Using the property from Step 2, we rewrite the second term:
\[ 2^{\log_{3} 7} - 7^{\log_{3} 2} = 2^{\log_{3} 7} - 2^{\log_{3} 7} \]

### Step 4: Simplify the expression
Now we see that both terms are equal:
\[ 2^{\log_{3} 7} - 2^{\log_{3} 7} = 0 \]

### Final Answer
Thus, the value of the expression \(2^{\log_{3} 7} - 7^{\log_{3} 2}\) is:
\[ \boxed{0} \]

---