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How many real values of x satisfy the equation sin(e^x) = 2^x + 2^(-x)?

1. 1
2. 0
3. 2
4. Infinitely many

Correct answer: 0

Solution

The left side sin(e^x) never exceeds 1, but the right side 2^x + 2^(-x) is always at least 2, so the two sides can never be equal; there are no real solutions.

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