Solve.

To solve the equation , we can express 64 as a power of 2. Since , we can rewrite the equation as . Because the bases are the same, we can set the exponents equal to each other, giving us .

Now, let’s explore this further.
Fun fact: The number 64 has a neat little history; it’s the smallest number that can be written as a power of two in two different ways: and also as since . This shows how numbers can camouflage in various forms!

Thinking about real-world applications, understanding powers of 2 is super useful in computing. Computers operate in binary (base 2), so concepts like megabytes and gigabytes relate directly to powers of 2; for example, a kilobyte is 1024 bytes, which is . So next time you’re saving a file, remember the amazing powers behind the bytes!