ข้อสอบคณิต 9 สามัญ - ปี 2563

$$\begin{gathered} \mathrm{จากคุณสมบัติของ} Log \\ 1) {\log }_{N^y}{M}^x = \frac{x}{y}{\log }_{N}M \\ 2) {\log }_{a}M-{\log }_{a}N = {\log }_a\left(\frac{M}{N}\right) \end{gathered}$$

$$\begin{gathered} \mathrm{จากโจทย์} \\ {\log }_{2}40-{\log }_{4}25 = {\log }_{2}40-{\log }_{2^2}{5}^2 \\ = {\log }_{2}40-\frac{\cancel{2}}{\cancel{2}}{\log }_{2}5 \\ = {\log }_{2}40-{\log }_{2}5 \\ = {\log }_2\left(\frac{40}{5}\right) \\ = {\log }_{2}8 = 3 \\ \mathrm{ดังนั้น} \mathrm{ตอบ} 4 \end{gathered}$$