SOLUTION: Solve the following equation log (2y) + Log (4y-1)=2

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Question 627187: Solve the following equation
log (2y) + Log (4y-1)=2

Found 2 solutions by hammy, josmiceli:
Answer by hammy(9) About Me  (Show Source):
You can put this solution on YOUR website!
log (2y) + log (4y-1) = 2
log [2y(4y-1)] = 2
log (8y^2 - 2y) = 2
10^2=8y^2 - 2y
100=8y^2 - 2y
0=2(4y^2-y-50)
y= [-(-1) +/- sqrt (-1)^2-4*4*(-50)]/ 2*4
y=[1 +/- (sqrt 1 + 800)]/8

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You must convert the right side into
a log expression.
Note that +log%28100%29+=+2+, so
+log%282y%29+%2B+Log%284y-1%29+=+2+
+log%282y%29+%2B+Log%284y-1%29+=+log%28100%29+
Since the general rule is: +log%28+a%2Ab+%29+=+log%28a%29+%2B+log%28b%29+
+log%28+%282y%29%2A%284y-1%29+%29+=+log%28100%29+
+%282y%29%2A%284y-1%29+=+100+
+8y%5E2+-+2y+=+100+
+8y%5E2+-+2y+-+100+=+0+
+4y%5E2+-+y+-+50+=+0+
Use quadratic formula
+y+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+4+
+b+=+-1+
+c+=+-50+
+y+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2+-+4%2A4%2A%28-50%29+%29%29%2F%282%2A4%29+
+y+=+%28+1+%2B-+sqrt%28+1+%2B+800+%29%29+%2F+8+
+y+=+%28+1+%2B-+28.302+%29+%2F+8+
+y+=+29.302%2F8+
+y+=+3.663+
and
+y+=+-27.302%2F8+
+y+=+-3.413+
check answers:
+log%282y%29+%2B+Log%284y-1%29+=+2+
Right away, I see the minus answer can't
work, since you can't have a log base 10
that gives a negative number
+log%28+2%2A3.663+%29+%2B+log%28+4%2A3.663+-+1+%29+=+2+
+log%28+7.326+%29+%2B+log%28+13.652+%29+=+2+
+.8649+%2B+1.1352++=+2+
+2.000096+=+2+
OK -error due to rounding off