A Common Tangent Exists

★ 7/10functions Extrema calculus Monotonicity Logarithms

Problem

Prove that when $a > \mathrm{e}^{1/\mathrm{e}}$ , the graphs of $f(x) = a^x$ and $g(x) = \log_a x$ have a common tangent line.

Answer

Solution

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

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