ข้อสอบคณิต 9 สามัญ - ปี 2559

$$\begin{gathered} \mathrm{สูตร}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\log }_{{\mathrm{n}}^{\mathrm{b}}}{\mathrm{m}}^{\mathrm{a}}=\frac{\mathrm{a}}{\mathrm{b}}\mathrm{logm} \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\log }_{\mathrm{n}}\mathrm{m}=\frac{1}{{\log }_{\mathrm{m}}\mathrm{n}} \end{gathered}$$

$$\begin{gathered} \mathrm{จากโจทย์} {\log }_{{\mathrm{a}}^2}\mathrm{b}=5 \\ \mathrm{จะได้} \frac{1}{2}{\log }_{\mathrm{a}}\mathrm{b}=5 \\ {\log }_{\mathrm{a}}\mathrm{b}=10 \\ \mathrm{ดังนั้น} {\log }_{{\mathrm{b}}^2}\mathrm{a}=\frac{1}{2}{\log }_{\mathrm{b}}\mathrm{a} \\ =\frac{1}{2}·\frac{1}{{\log }_{\mathrm{a}}\mathrm{b}} ; \mathrm{โดย} {\log }_a\mathrm{b}=10 \\ =\frac{1}{2}·\frac{1}{10} \\ =\frac{1}{20} \end{gathered}$$