経済学で出る数学

ワークブックでじっくり攻める：問 3.34

1. $ \log_{2}{3}=\dfrac{\log_{10}{3}}{\log_{10}{2}}=\dfrac{0.4771}{0.3010} \approx 1.59 $


2. $ \log_{5}{3}=\dfrac{\log_{10}{3}}{\log_{10}{5}}= \dfrac{\log_{10}{3}}{\log_{10}{({2^{-1}}\times 10)}} =\dfrac{\log_{10}{3}}{-\log_{10}{2}+{\log_{10}{10}}} =\dfrac{0.4771}{-0.3010+1} \approx 0.68 $


3. $ \log_{10}{5}={\log_{10}{({2^{-1}}\times 10)}} =-\log_{10}{2}+{\log_{10}{10}} =-0.3010+1 = 0.70 $


4. $ \log_{2}{5}=\dfrac{\log_{10}{5}}{\log_{10}{2}} =\dfrac{-\log_{10}{2}+{\log_{10}{10}}}{\log_{10}{2}} =\dfrac{-0.3010+1}{0.3010} \approx 2.32 $


5. $ \log_{1.05}{3}=\dfrac{\log_{10}{3}}{\log_{10}{1.05}}=\dfrac{0.4771}{0.02119} \approx 22.52 $


6. $ \log_{1.05}{10}=\dfrac{\log_{10}{10}}{\log_{10}{1.05}}=\dfrac{1}{0.02119} \approx 47.19 $