# 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

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