The constant term in the expansion of
`(log(x^(logx))-log_(x^(2))100)^(12)` is (base of lof is 10) `"_____"`.

Explanation

To find the constant term in the expansion of \( \left( \log(x^{\log x}) - \log_{x^2} 100 \right)^{12} \), we will follow these steps:

### Step 1: Simplify the expression inside the parentheses
We start with the expression \( \log(x^{\log x}) - \log_{x^2} 100 \).

Using the properties of logarithms:
1. \( \log(x^{\log x}) = \log x \cdot \log x = (\log x)^2 \)
2. \( \log_{x^2} 100 = \frac{\log 100}{\log(x^2)} = \frac{2}{\log x} \) (since \( \log 100 = 2 \))

Thus, we can rewrite the expression as:
\[ (\log x)^2 - \frac{2}{\log x} \]

### Step 2: Rewrite the expression in a suitable form
Let \( y = \log x \). Then the expression becomes:
\[ y^2 - \frac{2}{y} \]

To combine these terms, we can express it as:
\[ \frac{y^3 - 2}{y} \]

### Step 3: Raise the expression to the power of 12
Now we need to raise this expression to the power of 12:
\[ \left( \frac{y^3 - 2}{y} \right)^{12} = \frac{(y^3 - 2)^{12}}{y^{12}} \]

### Step 4: Identify the constant term
The constant term in the expansion of \( (y^3 - 2)^{12} \) can be found using the binomial theorem:
\[ (y^3 - 2)^{12} = \sum_{r=0}^{12} \binom{12}{r} (y^3)^r (-2)^{12-r} \]
This simplifies to:
\[ \sum_{r=0}^{12} \binom{12}{r} y^{3r} (-2)^{12-r} \]

To find the constant term in the overall expression \( \frac{(y^3 - 2)^{12}}{y^{12}} \), we need to find the term where the exponent of \( y \) is zero:
\[ 3r - 12 = 0 \implies r = 4 \]

### Step 5: Calculate the constant term
Now, substituting \( r = 4 \) into the binomial expansion:
\[ \text{Term} = \binom{12}{4} (y^3)^4 (-2)^{12-4} = \binom{12}{4} y^{12} (-2)^8 \]

The coefficient of this term is:
\[ \binom{12}{4} (-2)^8 \]

Calculating \( \binom{12}{4} \):
\[ \binom{12}{4} = \frac{12!}{4!(12-4)!} = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2 \times 1} = 495 \]

Now, \( (-2)^8 = 256 \).

Thus, the constant term is:
\[ 495 \times 256 \]

Calculating this gives:
\[ 495 \times 256 = 126720 \]

### Final Answer
The constant term in the expansion is \( 126720 \).