對數方程式(2)

意見反映

首頁 > > > >

解方程式 \({\rm{2}}{\left( {{{\log }_2}x} \right)^2} + 5\left( {{{\log }_2}x} \right) - 3 = 0\) ？

詳解：\({\rm{2}}{\left( {{{\log }_2}x} \right)^2} + 5\left( {{{\log }_2}x} \right) - 3 = 0\)

\(\left[ {{\rm{2}}\left( {{{\log }_2}x} \right) + 1} \right]\left[ {\left( {{{\log }_2}x} \right) - 3} \right] = 0\)

\({\log _2}x = - \frac{1}{2}\) , \({\log _2}x = 3\; \Rightarrow x = - \frac{1}{{\sqrt 2 }}\) , \(x = 8\)