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Find the number of integral solution of the equation `(log)_(sqrt(x))(x+|x-2|)=(log)_x(5x-6+5|x-2|)dot`

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Let `x+|x-2|=y`
`therefore"Equation becomes"log_(x)y^(2)=log_(x)(5y-6)impliesy^(2)=5y-6impliesy^(2)-5y+6=0impliesy=22 or 3 If y=2`
then `x+|x-2|=2 implies=ltxlt1uu1ltxle2If y=3`
then `x+|x-2|=3impliesx=5/2` only
Hence number of integral solutions is 1.]
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