如何得到小于或等于给定数字n的x的幂？

def power_less_than_or_equal(n, x):
    k = 0
    power = 1
    while power <= n:
        k += 1
        power = power * x
    return k - 1, x**(k - 1)

# 示例使用
n = 100
x = 2
result_k, result_power = power_less_than_or_equal(n, x)
print(f"小于或等于 {n} 的 {x} 的最大幂是 {result_power} (即 {x}^{result_k})")

import math

def power_less_than_or_equal_binary_search(n, x):
    if x == 1:
        return 0, 1
    low, high = 0, math.ceil(math.log(n, x))
    while low < high:
        mid = (low + high + 1) // 2
        if x ** mid <= n:
            low = mid
        else:
            high = mid - 1
    return low, x ** low

# 示例使用
n = 100
x = 2
result_k, result_power = power_less_than_or_equal_binary_search(n, x)
print(f"小于或等于 {n} 的 {x} 的最大幂是 {result_power} (即 {x}^{result_k})")