Always Positive, With a Log

★ 7/10functions Extrema calculus Monotonicity Logarithms

Problem

Let $f(x) = \mathrm{e}^x - a\ln(ax - a) + a$ with $a > 0$ . If $f(x) > 0$ holds for all $x$ in the domain, find the range of possible values of the real number $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Extrema, calculus, Monotonicity, Logarithms

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