Checking if a number is a valid power of 4 in JavaScript

We are required to write a JavaScript function that takes in a single integer, num, as the only argument. Our function should check whether this number is a valid power of 4 or not. If it is a power of 4, we should return true, false otherwise.

For example, if the input to the function is:

const num1 = 2356;
const num2 = 16;

Then the output should be:

const output1 = false;
const output2 = true;

Understanding Powers of 4

Powers of 4 are numbers that can be expressed as 4ⁿ where n is a non-negative integer:

• 4⁰ = 1
• 4¹ = 4
• 4² = 16
• 4³ = 64
• 4⁴ = 256

Method 1: Using Loop with Math.pow()

This approach iterates through possible powers of 4 and checks for a match:

const num1 = 2356;
const num2 = 16;

const isPowerOfFour = (num = 1) => {
    if (num  num) {
            break; // Optimization: stop if we exceed the number
        }
    }
    return false;
};

console.log(isPowerOfFour(num1));
console.log(isPowerOfFour(num2));

false
true

Method 2: Using Logarithms

A more mathematical approach using logarithms to check if log?(num) is a whole number:

const isPowerOfFourLog = (num) => {
    if (num 

true
true
true
true
false


Method 3: Using Division

Keep dividing by 4 until we can't divide evenly anymore:

const isPowerOfFourDivision = (num) => {
    if (num 

true
false


Comparison

Complete Example

// Test all methods with various inputs
const testNumbers = [1, 4, 8, 16, 64, 100, 256, 1024];

testNumbers.forEach(num => {
    console.log(`${num}: ${isPowerOfFourDivision(num)}`);
});

1: true
4: true
8: false
16: true
64: true
100: false
256: true
1024: true

Conclusion

The division method is generally the most reliable approach for checking powers of 4, as it avoids floating-point precision issues and works efficiently for numbers of any size. The logarithmic method is fastest but may have precision limitations with very large numbers.