Use common logarithms or natural logarithms and a calculator to evaluate the expression. \( \log _{0.5} 12.3 \) Evaluate the expression. \( \log _{0.5} 12.3 \approx \square \) (Type an integer or a decimal. Do not round until the final answer. Then round to four decimal places as needed.)

To evaluate \( \log_{0.5} 12.3 \), we can use the change of base formula for logarithms: \[ \log_{a} b = \frac{\log_{c} b}{\log_{c} a} \] Using common logarithms (base 10), we can rewrite the expression as: \[ \log_{0.5} 12.3 = \frac{\log(12.3)}{\log(0.5)} \] Now, using a calculator, we find: - \( \log(12.3) \approx 1.0899 \) - \( \log(0.5) \approx -0.3010 \) Thus, substituting these values gives us: \[ \log_{0.5} 12.3 \approx \frac{1.0899}{-0.3010} \approx -3.6187 \] Rounding this result to four decimal places, we have: \[ \log_{0.5} 12.3 \approx -3.6187 \] So the final answer is: -3.6187