SOLUTION: I am lost on this one Solve ln(3x+7)+lnx=ln6 Thank you

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Question 61746: I am lost on this one

Solve ln(3x+7)+lnx=ln6
Thank you
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
ln(3x+7) + lnx = ln6
or ln((3x+7)*x) - ln6 = 0
or ln((3x+7)*x/6) = 0

This means,
log%28e%2C%28%283x%2B7%29%2Ax%2F6%29%29+=+0
or %283x%2B7%29%2Ax%2F6+=+e%5E0+=+1
or %283x%2B7%29%2Ax+=+6
or 3x%5E2+%2B+7x+-+6+=+0
or 3x%5E2+%2B+9x+-+2x+-+6+=+0
or 3x%28x+%2B+3%29+-+2%28x+%2B+3%29+=+0
or %283x-2%29%28x+%2B+3%29+=+0

Either or 3x+-+2+=+0 or x+%2B+3+=+0
i.e. either x+=+2%2F3 or x+=+-3

But, logarithm of a negative number is not defined. If x+=+-3 then log%28e%2Cx%29+=+log%28e%2C-3%29 becomes undefined. So x cannot be -3.
Thus x+=+2%2F3 is the only solution.