SOLUTION: log (6x + 5) - log 3 = log 2 - log x

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Question 4895: log (6x + 5) - log 3 = log 2 - log x
Found 2 solutions by rapaljer, arunpaul:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28%286x%2B5%29%2F3%29=log+%282%2Fx%29

If log M = log N, then M = N, so
+%286x%2B5%29%2F3+=+2%2Fx

Multiply both sides by the common denominator which is 3x:
%283x%29%2A%286x%2B5%29+%2F3+=+%283x%29%2A2%2Fx+
x%2A%286x%2B5%29++=+3%2A2+
6x%5E2+%2B+5x+=+6
6x%5E2+%2B+5x+-+6+=+0
+%283x+-+2%29%282x+%2B+3%29+=+0
x+=+2%2F3+ x+=+-3%2F2
The second solution is not allowed since the log of negative is not allowed in the real number system.

Final answer: x=2%2F3
R^2 at SCC

Answer by arunpaul(104) About Me  (Show Source):
You can put this solution on YOUR website!
log (6x + 5) - log 3 = log 2 - log x
log (6x + 5) +log x = log 2+log 3
log ((6x + 5)*x)= log (2*3)
taking the anti log we have
(6x+5)*x = 2*3
6x^2+5x-6 =0
putting it in solution of quadratic equation the solution = .667 and -1.5
since log( -1.5 ) is undefined, only 0.667 is the solution.