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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.**** \(\frac{1}{{{e^2}}}.\)**

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**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 **\({x_1}. {x_2} = \frac{1}{{{e^2}}}}.\)**