Python: Find an integer exponent x such that a^x = n

Last update on May 30 2025 11:48:56 (UTC/GMT +8 hours)

Find Integer Exponent

Write a Python program to find an integer exponent x such that a^x = n.

Input:
a =  2 : n =  1024
Output:
10
Input:
a =  3 : n =  81

Output:
4
Input:
a =  3 : n =  1290070078170102666248196035845070394933441741644993085810116441344597492642263849

Output:
170

Visual Presentation:

Sample Solution:

Python Code:

# Define a function named 'test' that takes two parameters, n and a
# The function finds an integer exponent x such that a^x = n
def test(n, a):
    # Initialize variables m and x
    m = 1
    x = 0
    
    # Use a while loop to find the exponent x
    while m != n:
        # Increment x and update m by multiplying it with a
        x += 1
        m *= a
    
    # Return the found exponent x
    return x

# Set values for variables a and n
a = 2
n = 1024
# Print a message indicating the values of a and n
print("a = ", a, ": n = ", n)
# Print a message indicating the task and the result of the test function
print("Find an integer exponent x such that a^x = n:")
# Print the result of the test function applied to the given values of a and n
print(test(n, a))

# Set new values for variables a and n
a = 3
n = 81
# Print a message indicating the values of a and n
print("\na = ", a, ": n = ", n)
# Print a message indicating the task and the result of the test function
print("Find an integer exponent x such that a^x = n:")
# Print the result of the test function applied to the new values of a and n
print(test(n, a))

# Set new values for variables a and n (large integer)
a = 3
n = 1290070078170102666248196035845070394933441741644993085810116441344597492642263849
# Print a message indicating the values of a and n
print("\na = ", a, ": n = ", n)
# Print a message indicating the task and the result of the test function
print("Find an integer exponent x such that a^x = n:")
# Print the result of the test function applied to the new values of a and n
print(test(n, a))

Sample Output:

a =  2 : n =  1024
Find an integer exponent x such that a^x = n:
10
a =  3 : n =  81

Find an integer exponent x such that a^x = n:
4
a =  3 : n =  1290070078170102666248196035845070394933441741644993085810116441344597492642263849

Find an integer exponent x such that a^x = n:
170

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to compute the smallest integer exponent x such that a raised to x equals n using iterative multiplication.
• Write a Python program to determine if an integer exponent exists for a given a and n, returning -1 if not.
• Write a Python program to calculate the exponent by applying math.log and then verifying with integer rounding.
• Write a Python program to implement a loop that multiplies a repeatedly until it equals n and count the iterations as x.

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• Python Puzzles Exercises Home ↩
• Python Exercises Home ↩

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Python Code Editor :

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