ข้อสอบคณิต 9 สามัญ - ปี 2556

$$\begin{gathered} \mathrm{สูตร} \log {\log }_n m=\frac{\log m}{\log n} \\ \log m^n=n \log m \\ \mathrm{จากโจทย์} \left({\log }_7 625\right)\left({\log }_5 343\right) \end{gathered}$$

$$\begin{gathered} \mathrm{จะได้} \left({\log }_7 625\right)\left({\log }_5 343\right)=\left(\frac{\log 625}{\log 7}\right)\left(\frac{\log 343}{\log 5}\right) \\ =\left(\frac{\log 5^4}{\log 7}\right)\left(\frac{\log 7^3}{\log 5}\right) \\ =\left(\frac{4 \bcancel{\log 5}}{\cancel{\log 7}}\right)\left(\frac{3\cancel{ \log 7}}{\bcancel{\log 5}}\right) \\ =4\left(3\right) \\ =12 \\ \mathrm{ดังนั้น} ({\log }_7 625)({\log }_5 343)=12 \end{gathered}$$