If \( \log _{3} 41 \approx 3.38 \) and \( \log _{3} 2 \approx 0.631 \), what is \( \log _{3} 82 \), to the nearest thousandth? (1 point) Check answer Remaining Attempts : 3

To find \( \log_{3} 82 \), we can express 82 as \( 2 \times 41 \). Using the properties of logarithms, we can calculate: \[ \log_{3} 82 = \log_{3} (2 \times 41) = \log_{3} 2 + \log_{3} 41 \] Now we can substitute the given approximate values: \[ \log_{3} 82 \approx \log_{3} 2 + \log_{3} 41 \approx 0.631 + 3.38 \] Adding these values together: \[ \log_{3} 82 \approx 0.631 + 3.38 = 4.011 \] Now, rounding to the nearest thousandth, we find: \[ \log_{3} 82 \approx 4.011 \] So the final answer is \( \boxed{4.011} \).