The value of `(1)/(log_(2)pi)+(1)/(log_(6)pi)` is greater than `2` .
(a) True (b) False

Answer

To solve the problem, we need to evaluate the expression \(\frac{1}{\log_2 \pi} + \frac{1}{\log_6 \pi}\) and determine if it is greater than 2.

### Step-by-Step Solution:

1. **Use Change of Base Formula**:
We can rewrite the logarithms using the change of base formula:
\[ \log_a b = \frac{\log_c b}{\log_c a} \]
So we have:
\[ \log_2 \pi = \frac{\log \pi}{\log 2} \quad \text{and} \quad \log_6 \pi = \frac{\log \pi}{\log 6} \]

2. **Substitute into the Expression**:
Substitute these into the original expression:
\[ \frac{1}{\log_2 \pi} = \frac{\log 2}{\log \pi} \quad \text{and} \quad \frac{1}{\log_6 \pi} = \frac{\log 6}{\log \pi} \]
Therefore, we can rewrite the expression as:
\[ \frac{\log 2}{\log \pi} + \frac{\log 6}{\log \pi} = \frac{\log 2 + \log 6}{\log \pi} \]

3. **Combine the Logs**:
Using the property of logarithms that states \(\log a + \log b = \log(ab)\), we combine the logs:
\[ \log 2 + \log 6 = \log(2 \times 6) = \log 12 \]
Thus, the expression simplifies to:
\[ \frac{\log 12}{\log \pi} \]

4. **Inequality Setup**:
We need to check if:
\[ \frac{\log 12}{\log \pi} > 2 \]
This can be rearranged to:
\[ \log 12 > 2 \log \pi \]
Using the property of logarithms, we can rewrite \(2 \log \pi\) as:
\[ 2 \log \pi = \log(\pi^2) \]
Therefore, we need to check if:
\[ \log 12 > \log(\pi^2) \]
This implies:
\[ 12 > \pi^2 \]

5. **Evaluate the Inequality**:
Now, we need to evaluate whether \(12\) is greater than \(\pi^2\). We know that:
\[ \pi \approx 3.14 \implies \pi^2 \approx 9.86 \]
Hence:
\[ 12 > 9.86 \quad \text{(True)} \]

6. **Conclusion**:
Since \(12 > \pi^2\) is true, we conclude that:
\[ \frac{1}{\log_2 \pi} + \frac{1}{\log_6 \pi} > 2 \]
Therefore, the statement is **True**.

### Final Answer:
(a) True