Two Solutions of a Mixed Equation

★ 8/10functions Extrema calculus Monotonicity Logarithms

Problem

The equation

\mathrm{e}^{x+m} - (\mathrm{e} - 2)\ln x - \ln^2 x - (m + 2) = 0

has exactly two real solutions. Find the range of $m$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Extrema, calculus, Monotonicity, Logarithms

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