SOLUTION: can somone plese help me solve this? log(9, sqrt x ) + log(9, sqrt 2x+3)=1/2

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Question 61660: can somone plese help me solve this?
log(9, sqrt x ) + log(9, sqrt 2x+3)=1/2
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
log%289%2Csqrt%28x%29%29++%2B+log%289%2Csqrt%282x%2B3%29%29+=+1%2F2
or log%289%2Csqrt%28x%29%2Asqrt%282x%2B3%29%29+=+1%2F2
or log%289%2Csqrt%28x%2A%282x%2B3%29%29%29+=+1%2F2
or log%289%2C%282x%5E2%2B3x%29%5E%281%2F2%29%29+=+1%2F2
or %281%2F2%29log%289%2C%282x%5E2%2B3x%29%29+=+1%2F2
or log%289%2C%282x%5E2%2B3x%29%29+=+1
or 2x%5E2%2B3x+=+9%5E1
or 2x%5E2+%2B+3x+-+9+=+0
or 2x%5E2+%2B+6x+-+3x+-+9+=+0
or 2x%28x+%2B+3%29+-+3%28x+%2B+3%29+=+0
or %282x+-+3%29%28x+%2B+3%29+=+0
Either or 2x+-+3+=+0 or x+%2B+3+=+0
i.e. either x+=+3%2F2 or x+=+-3

But, square root of a negative number is not defined. If x+=+-3 then sqrt%28x%29+=+sqrt%28-3%29 becomes undefined. So x cannot be -3.
Thus x+=+3%2F2 is the only solution.