Python guessing game exercise - confused about the description and the math

My questions are on the bottom.

This exercise is based on a guessing game where the user (you) inputs a lower and upper bound int and then the PC picks a random number within those boundaries. Your job is to guess the number and the program tells the user if the guess is greater than, less than, or equal to the number the PC has chosen. It's most strategic to make guesses from the middle. The number of tries is recorded.

Here is the code:

import random

smaller = int(input("Enter the smaller number: "))
larger = int(input("Enter the larger number: "))
myNumber = random.randint(smaller, larger)

count = 0
while True:
   count += 1
   userNumber = int(input("Enter your guess: "))
   if userNumber < myNumber:
       print("Too small!")

   elif userNumber > myNumber:
       print("Too large!")

   else:
       print("Congratulations! You've got it in", count, "tries!")
       break

Here is a sample output:

#Output example
Enter the smaller number: 1
Enter the larger number: 100
Enter your guess: 50
Too small!
Enter your guess: 75
Too large!
Enter your guess: 63
Too small!
Enter your guess: 69
Too large!
Enter your guess: 66
Too large
Enter your guess: 65
You've got it in 6 tries!

Now here is the exercise description:

"Modify the guessing-game program so that the user thinks of a number that the computer must guess.

The computer must make no more than the minimum number of guesses, and it must prevent the user from cheating by entering misleading hints.

Use I'm out of guesses, and you cheated and Hooray, I've got it in X tries as your final output.

(Hint: Use the math.log function to compute the minimum number of guesses needed after the lower and upper bounds are entered.)"

Here are two sample outputs I should be able to reproduce:

Enter the smaller number: 0
Enter the larger number: 10

0 10
Your number is 5
Enter =, <, or >: <
0 4
Your number is 2
Enter =, <, or >: >
3 4
Your number is 3
Enter =, <, or >: =
Hooray, I've got it in 3 tries!

and

Enter the smaller number: 0
Enter the larger number: 50
0 50
Your number is 25
Enter =, <, or >: <
0 24
Your number is 12
Enter =, <, or >: <
0 11
Your number is 5
Enter =, <, or >: <
0 4
Your number is 2
Enter =, <, or >: <
0 1
Your number is 0
Enter =, <, or >: >
1 1
Your number is 1
Enter =, <, or >: >
I'm out of guesses, and you cheated!

Now here is my code:

from math import log2

#get the lower and upper bounds that the PC can guess between
smaller = int(input("Enter the smaller number: "))
larger = int(input("Enter the larger number: "))

#this should calculate the maximum number of tries the PC can do
max_tries = round(log2(larger-smaller+1))
print("PC should guess in no more than %s tries\n" % max_tries)

count = 0
while count <= max_tries:
    count += 1
    pc_guess = (larger+smaller) // 2 #This is the PC's guess
    print("%d %d" % (smaller, larger)) #boundry
    print("Your number is ", pc_guess) #printing PC's guess

    op = input("Enter =, <, or >: ") #giving PC more info
    
    if op == '<': #the number is less than the PC's guess
        larger = pc_guess - 1

    elif op == '>': #the number is greater than the PC's guess
        smaller = pc_guess + 1

    elif op == '=':
        print("Hooray I've got it in", count, "tries")#PC guessing correct
        break

if count > max_tries:
    print("I'm out of guesses, and you cheated")

Am I even thinking about this exercise correctly?

Furthermore, I don't understand how to get the PC to get the right answer in "no more than the minimum number of guesses," which I calculated as log2(larger-smaller+1) in my code. Calculating the average of the upper and lower bound still results in greater tries than the log2 result.

Also, am I even calculating the PC's best guess correctly (the average calculation)?

I think that it would help you a lot if you rounded up the result, so as to get one more possible hint. Like this:

import math
.
.
.
max_tries = math.ceil(math.log(larger-smaller))

You can see more details on this post, too: https://stackoverflow.com/questions/60068321/guessing-game-in-python-wont-print-elseif