def ceil_log(number: int, base: int) -> int:
    """Compute max(1, ceil(log(number, base))).

    Use only integer arithmetic in order to avoid numerical error.
    """
    if number < 1 or base < 2:
        raise ValueError("math domain error")
    result = 1
    accum = base
    while accum < number:
        result += 1
        accum *= base
    return result