経済学で出る数学

ワークブックでじっくり攻める：問 3.32

1. $\log_{e}{\left(e^{\alpha x}e^{\beta y}\right)}= \log_{e}{e^{\alpha x}}+\log_{e}{e^{\beta y}}= {\alpha x}\log_{e}{e}+{\beta y}\log_{e}{e} ={\alpha x}+{\beta y} $


2. $\log_{e}{\left(\alpha e^{\beta}\right)}= \log_{e}{\alpha}+{\beta}\log_{e}{e} =\log_{e}{\alpha}+{\beta} $


3. $\log_{a}{\left(x\right)^{\alpha}\left(x\right)^{\beta}}= \log_{a}{\left(x\right)^{\alpha}}+\log_{a}{\left(x\right)^{\beta}}= {\alpha}\log_{a}{x}+{\beta}\log_{a}{x} =(\alpha + \beta)\log_{a}{x} $


4. $ e^{{\alpha}\log_{e}{e^x}+{\beta}\log_{e}{e^y}}= e^{{\alpha}x\log_{e}{e}+{\beta}y\log_{e}{e}}= e^{{\alpha}x+{\beta}y} $