1.

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

Answer»

Solution :
`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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