SOLUTION: log4(b+27)-log4(b-7)=log4b

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Question 810861: log4(b+27)-log4(b-7)=log4b
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+4%2C%28b%2B27%29+%29+-+log%28+4%2C%28b-7%29+%29+=+log%28+4%2Cb+%29+
+log%28+4%2C+%28+b+%2B+27+%29+%2F+%28+b+-+7+%29+%29+=+log%28+4%2Cb+%29+
++%28+b+%2B+27+%29+%2F+%28+b+-+7+%29+%29+=+b+
+b+%2B+27+=+b%2A%28+b+-+7+%29+
+b+%2B+27+=+b%5E2+-+7b+
+b%5E2+-+8b+-+27+=+0+
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ( I'll use x instead of b )
+a+=+1+
+b+=+-8+
+c+=+-27+
x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A%28-27%29+%29%29%2F%282%2A1%29+
x+=+%28+8+%2B-+sqrt%28+64+%2B+108+%29%29+%2F+2+
x+=+%28+8+%2B-+sqrt%28+172+%29%29+%2F+2+
+x+=+%28+8+%2B+2%2Asqrt%2843%29+%29+%2F+2+
+b+=++4+%2B+sqrt%2843%29+
and
+b+=+4+-+sqrt%2843%29+
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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
log4(b+27)-log4(b-7)=log4b
log4(b+27) = log4(b-7)+log(4b)
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log4(b+27) = log[4b^2-28b]
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b+27 = 4b^2-28b
----
4b^2 -29b -27 = 0
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Positive solution:
b = 8.0849
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Cheers,
Stan H.
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