Python - Concatenate Numbers of Varying Bases

app.py

import math

def join_number(a: int, b: int, base: int) -> int:
    return a * base ** math.ceil(math.log(b, base)) + b

assert join_number(2, 3, 10) == 23
assert join_number(4, 64, 10) == 464
assert join_number(573, 82, 10) == 57382

assert join_number(0b101, 0b111, 2) == 0b101111
assert join_number(0b1100, 0b100111, 2) == 0b1100100111
assert join_number(0b1010011, 0b1100100, 2) == 0b10100111100100

assert join_number(0xA4, 0xB3, 16) == 0xA4B3
assert join_number(0xFE, 0xDEAD, 16) == 0xFEDEAD
assert join_number(0xBEEF48C1, 0xA2E6, 16) == 0xBEEF48C1A2E6

assert join_number(0o3, 0o7, 8) == 0o37
assert join_number(0o3, 0o753, 8) == 0o3753
assert join_number(0o1234567, 0o7216534, 8) == 0o12345677216534