\( \left. \begin{array} { l | l } { .2 .2 } & { 2 ^ { x } = 64 } \\ \hline \end{array} \right. \)

To solve the equation \( 2^x = 64 \), we can express 64 as a power of 2. Since \( 64 = 2^6 \), we rewrite the equation as \( 2^x = 2^6 \). By equating the exponents, we find that \( x = 6 \). So, the solution to the equation is \( x = 6 \). Isn't it fascinating how exponents work? They form the backbone of exponential growth in many situations, including population modeling and finance! From baking—where doubling a recipe can necessitate understanding exponential increases—to computer science, where data structures can require efficient algorithms based on powers of 2, these concepts seep into everyday life in surprising ways!