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Find the number of solutions to `log_(e) |sin x| = -x^(2) + 2x` in `[-(pi)/(2), (3pi)/(2)]`.

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`log_(e)|sin x| = -x(x - 2)`
Graphs of `y = log_(e)|sin x|` and `y = -x(x - 2)` meet exactly four times in `[-(pi)/(2), (3pi)/(2)],`
hence four roots.
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