Create is_power_of_four_logarithm.py

maths/is_power_of_four_logarithm.py

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+import math
+
+
+def is_power_of_four_logarithm(num: int) -> bool:
+    """
+    Check if a given number is a power of four using logarithms.
+
+    Args:
+        num (int): The number to be checked.
+
+    Returns:
+        bool: True if the number is a power of 4, False otherwise.
+
+    Raises:
+        ValueError: If the input number is not positive.
+    """
+    if num <= 0:
+        raise ValueError("Input number must be positive")
+
+    # Calculate the logarithm base 4 of the number
+    log_base_4 = math.log(num, 4)
+
+    # Check if the result is an integer
+    return log_base_4.is_integer()
+
+
+# Test cases
+if __name__ == "__main__":
+    num1 = 16  # 4^2 = 16
+    num2 = 4096  # 4^6 = 4096
+    num3 = 18  # Not a power of 4
+
+    print(f"{num1} is a power of 4: {is_power_of_four_logarithm(num1)}")
+    print(f"{num2} is a power of 4: {is_power_of_four_logarithm(num2)}")
+    print(f"{num3} is a power of 4: {is_power_of_four_logarithm(num3)}")