import math


def calculate_y(x):
    y = (10 * math.log(x + 1) + 30) * math.sqrt(x)
    return y


def reduce_index(index):
    # Define the function to find the root of
    def f(x):
        return (10 * math.log(x + 1) + 30) * math.sqrt(x) - index

    # Set the initial bounds for the bisection method
    a = 0
    b = 1e6

    # Set the tolerance for the root-finding algorithm
    tol = 1e-6

    # Perform the bisection method to find the root
    while (b - a) / 2 > tol:
        c = (a + b) / 2
        if f(c) == 0:
            return c
        elif f(a) * f(c) < 0:
            b = c
        else:
            a = c

    return (a + b) / 2


# Example usage
y = 100000
x = reduce_index(y)
print(x)