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Algebra Level 3

For some constant $a> 1$ , the two functions $f(x) = a^x$ and $g(x) = \log_a x$ intersect exactly once.

What is $a?$

e^{1 }

e^{ -1 }

e^{e }

e^{ -e }

e^{ \frac{1}{e} }

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by Prince Loomba

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