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Find the total number of solutions to si...

Find the total number of solutions to `sinpi x=|ln|x||`.

Text Solution

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We have `sinpix=|In|x||" "(i)`
To find the roots of Eq.(i), we draw the graphs of `y=sinpixandy=|In|x||` and find their points of intersection.
Graph of `y=sinpix` is a simple sine curve with period '2.
The graphs of both functions are as shown in the following figure.

From the above figure, the number of roots of Eq. (i) is '6'.
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