Statement-1(Assertion) and Statement-2 (reason) Each of these question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below.
(a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1
Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement -1
(c) Statement -1 is true, Statement -2 is false
(d) Statement -1 is false, Statement -2 is true
Statement -1 The equation `(logx)^2+logx^2-3=0` has two distinct solutions.
Statement-2 `logx^(2)`=2logx.

Answer

To solve the problem, we need to analyze both statements and determine their truth values.

### Step-by-Step Solution:

1. **Analyze Statement-1**:
The equation given is \((\log x)^2 + \log x^2 - 3 = 0\).
We can use the logarithmic property that states \(\log x^2 = 2 \log x\).

Substituting this into the equation gives:
\[ (\log x)^2 + 2 \log x - 3 = 0 \]
Let \(y = \log x\). The equation now becomes:
\[ y^2 + 2y - 3 = 0 \]

2. **Factor the Quadratic Equation**:
We can factor the quadratic equation:
\[ (y + 3)(y - 1) = 0 \]
This gives us the solutions:
\[ y + 3 = 0 \quad \Rightarrow \quad y = -3 \]
\[ y - 1 = 0 \quad \Rightarrow \quad y = 1 \]

3. **Convert Back to Logarithmic Form**:
Recall that \(y = \log x\):
- For \(y = 1\):
\[ \log x = 1 \quad \Rightarrow \quad x = 10^1 = 10 \]
- For \(y = -3\):
\[ \log x = -3 \quad \Rightarrow \quad x = 10^{-3} = 0.001 \]

4. **Determine the Number of Distinct Solutions**:
We found two solutions: \(x = 10\) and \(x = 0.001\). Therefore, Statement-1 is **true** because the equation has two distinct solutions.

5. **Analyze Statement-2**:
Statement-2 states that \(\log x^2 = 2 \log x\). This is a fundamental property of logarithms and is always true.

6. **Conclusion**:
- Statement-1 is **true**.
- Statement-2 is **true**.
- However, Statement-2 is indeed a correct explanation for Statement-1.

### Final Answer:
The correct choice is (a): Statement-1 is true, Statement-2 is true, and Statement-2 is a correct explanation for Statement-1.