1a) Evaluate \( \frac{\log 25-\log 125+\frac{1}{2} \log 625}{3 \log 5} \)

Calculate or simplify the expression \( (\log 25-\log 125+\frac{1}{2} \log 625)/(3 \log 5) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\log_{10}{\left(25\right)}-\log_{10}{\left(125\right)}+\frac{1}{2}\log_{10}{\left(625\right)}\right)}{\left(3\log_{10}{\left(5\right)}\right)}\) - step1: Remove the parentheses: \(\frac{\log_{10}{\left(25\right)}-\log_{10}{\left(125\right)}+\frac{1}{2}\log_{10}{\left(625\right)}}{3\log_{10}{\left(5\right)}}\) - step2: Multiply: \(\frac{\log_{10}{\left(25\right)}-\log_{10}{\left(125\right)}+\frac{\log_{10}{\left(625\right)}}{2}}{3\log_{10}{\left(5\right)}}\) - step3: Calculate: \(\frac{\log_{10}{\left(5\right)}}{3\log_{10}{\left(5\right)}}\) - step4: Rewrite in terms of common logarithms: \(\frac{\log_{10}{\left(5\right)}}{\log_{10}{\left(5^{3}\right)}}\) - step5: Use the logarithm base change rule: \(\log_{5^{3}}{\left(5\right)}\) - step6: Simplify the expression: \(\frac{1}{3}\) The value of \( \frac{\log 25-\log 125+\frac{1}{2} \log 625}{3 \log 5} \) is approximately 0.3.