recursively calculate if x is power of b

The assignment is to write a recursive function that receives 2 whole non-negative numbers b, x, and returns True if there’s a natural integer n so that b**n=x and False if not. I’m not allowed to use any math operators or loops, except % to determine if a number is even or odd.
but i do have external functions that i can use. Which can add 2 numbers, multiply 2 numbers, and divides a number by 2. also i can write helper function that i can use in the main function.

this is what i got so far, but it only works if b is in the form of 2^y (2,4,8,16 etc)

def is_power(b, x):
    if b == x:
        return True
    if b > x:
        return False
    return is_power(add(b, b), x)  # the func 'add' just adds 2 numbers

Furthermore, the complexity needs to be O(logb * logx)
Thank you.

>Solution :

You can essentially keep multiplying b by b until you reach, or pass, n.

A recursive implementation of this, using a helper function, could look something like this:

def is_power(b, x):
    if b == 1:          # Check special case
        return x == 1
    return helper(1, b, x)

def helper(acc, b, x):
    if acc == x:
        return True
    elif acc > x:
        return False
    else:
        return helper(mul(acc, b), b, x)