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The solution of the equation (log)7(log)...

The solution of the equation `(log)_7(log)_5(sqrt(x+5)+sqrt(x)=0` is...

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The correct Answer is:
4
Given equation is
`log_(7)log_(5)(sqrt(x+5)+sqrt(x))=0 rArr log_(5)(sqrt(x+5)+sqrt(x))=1`
`rArr sqrt(x+5)+sqrt(x)=5 rArr sqrt(x+5) =5-sqrt(x)`
`rArr x+5=25+x-10sqrt(x) rArr 10sqrt(x)=20 rArr sqrt(x) =2`
`therefore x=4`
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