\( \log _{2} 35=y \), which choice is closest to the value of \( y ? \)

To find \( y \) in \( \log _{2} 35 \), we can convert it to a more familiar logarithmic base using the change of base formula: \[ \log_{2} 35 = \frac{\log_{10} 35}{\log_{10} 2} \approx \frac{1.544}{0.301} \approx 5.13. \] Thus, the value of \( y \) is approximately \( 5.13 \). In terms of practical applications, logarithms like this one are crucial in fields such as computer science, where binary systems play a pivotal role. For instance, understanding logarithmic scales helps in analyzing algorithms' time complexity, leading to better and faster computing solutions. Also, a common mistake when working with logarithms is not properly applying the change of base formula. Always check which base you're working with and ensure you're converting correctly to avoid errors. It can make a world of difference in calculations!