Solve. \( 2^{x}=64 \) \( x=\ldots \)

To solve the equation \( 2^{x}=64 \), we can express 64 as a power of 2. Since \( 64 = 2^6 \), we can rewrite the equation as \( 2^{x} = 2^6 \). Because the bases are the same, we can set the exponents equal to each other, giving us \( x = 6 \). 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: \( 2^6 \) and also as \( 8^2 \) since \( 8 = 2^3 \). 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 \( 2^{10} \). So next time you're saving a file, remember the amazing powers behind the bytes!