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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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