c) \( \log _{2} \sqrt[3]{7} \)

To simplify \( \log _{2} \sqrt[3]{7} \), we can first convert the expression into a fraction: \( \sqrt[3]{7} \) is the same as \( 7^{1/3} \). Thus, we rewrite the logarithm as: \[ \log_{2} \sqrt[3]{7} = \log_{2} (7^{1/3}) = \frac{1}{3} \log_{2} (7) \] This means you can break down more complex logarithmic expressions into simpler parts, making calculations easier! The logarithm has been a crucial tool in mathematics since its invention by John Napier in the early 17th century. Initially used for simplifying multiplication and division into addition and subtraction, logs have evolved into a fundamental concept across various fields, like engineering, computer science, and finance, showcasing their timeless utility!