adsense
Product of all solutions of the equation \({\ln ^2}x + 2\ln x – 3 = 0\) equal
A. \(\frac{1}{{{e^3}}}.\)
B. \( – 2\).
C. \( – 3.\)
D. \(\frac{1}{{{e^2}}}.\)
adsense
The answer:
Choose EASY
We have: \({\ln ^2}x + 2\ln x – 3 = 0 \Leftrightarrow \left\{ \begin{array}{l}x > 0\\\left( {\ln x – 1} \right) \left( {\ln x + 3} \right)\end{array} \right.\Leftrightarrow \left\{ \begin{array}{l}x > 0\\\left[\begin{array}{l}x=e\\x={e^{–3}}\end{array}\right\end{array}\right\Leftrightarrow\left[\begin{array}{l}x=e\\x={e^{–3}}\end{array}\right\)[\begin{array}{l}x=e\x={e^{–3}}\end{array}\right\end{array}\right\Leftrightarrow\left[\begin{array}{l}x=e\x={e^{–3}}\end{array}\right\)
So \({x_1}. {x_2} = \frac{1}{{{e^2}}}}.\)
