------
## 最终结论
```python
def change_base(x: int, base: int):
    """Change numerical base of input number x to base.
    return string representation after the conversion.
    base numbers are less than 10.
    >>> change_base(8, 3)
    '22'
    >>> change_base(8, 2)
    '1000'
    >>> change_base(7, 2)
    '111'
    """
    
    # Check input validity
    if not isinstance(x, int) or x < 0:
        raise ValueError("Input number x must be a non-negative integer.")
    if not isinstance(base, int) or base < 2 or base > 9:
        raise ValueError("Base must be an integer between 2 and 9.")
    
    # Initialize result string and remainder list
    result = ""
    remainders = []
    
    # Perform base conversion
    while x > 0:
        remainders.append(x % base)
        x //= base
    
    # Build result string
    for remainder in reversed(remainders):
        result += str(remainder)
    
    return result if result else "0"
```