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

Python Programming Puzzles: Exercise-56 with Solution

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

Pictorial Presentation:

Sample Solution:

Python Code:

def test(n,a):
    m = 1
    x = 0
    while m != n:
        x += 1
        m *= a
    return x

a = 2
n = 1024
print("a = ",a,": n = ",n)
print("Find an integer exponent x such that a^x = n:")    
print(test(n,a))
a = 3
n = 81
print("a = ",a,": n = ",n)
print("\nFind an integer exponent x such that a^x = n:")    
print(test(n,a))
a = 3
n = 1290070078170102666248196035845070394933441741644993085810116441344597492642263849
print("a = ",a,": n = ",n)
print("\nFind an integer exponent x such that a^x = 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:

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