Find the value of \( \log \frac{1}{2} \) rounded to the nearest thousandth. -0.300 0.301 0.302 -0.301

To find \( \log \frac{1}{2} \), we can use the property of logarithms that states \( \log \frac{a}{b} = \log a - \log b \). Therefore: \[ \log \frac{1}{2} = \log 1 - \log 2 \] Since \( \log 1 = 0 \), this simplifies to: \[ \log \frac{1}{2} = 0 - \log 2 = -\log 2 \] Now, we need to find the value of \( \log 2 \). The approximate value of \( \log 2 \) (base 10) is about 0.301. Consequently: \[ \log \frac{1}{2} \approx -0.301 \] Rounding to the nearest thousandth gives us: \[ \log \frac{1}{2} \approx -0.301 \] Thus, the value of \( \log \frac{1}{2} \) rounded to the nearest thousandth is \( -0.301 \). The correct answer is: -0.301