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Find the number of solutions to 7^|x|(|1...

Find the number of solutions to `7^|x|(|1-|x||)=1`.

Text Solution

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We have `7^|x|(|1-|x||)=1`
or `|1-|x||=7^(-|x|)`
To find the number of solutions to the equation, we draw the graph of `y=|1-|x||andy=7^(-|x|)` and find number of points of intersection. The graphs of both the functions are as intersection.
The graphs of both the functions are as shown in the following figure.

From the graph, the number of solutions is 5.
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