SOLUTION: Log6(x+5)+log6(x+4)=2

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Question 697789: Log6(x+5)+log6(x+4)=2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The trick here is to express +2+ as a log
to the base +6+:
+2+=+log%286%2C36%29+
----------------
given:
+log%28+6%2C%28+x%2B5+%29+%29+%2B+log%28+6%2C%28+x+%2B+4+%29+%29+=+log%28+6%2C+36+%29+
+log%28+6%2C+%28+x%2B5+%29%2A%28+x%2B4+%29+%29+=+log%28+6%2C+36+%29+
+%28+x%2B5+%29%2A%28+x%2B4+%29+=+36+
+x%5E2+%2B+9x+%2B+20+=+36+
+x%5E2+%2B+9x+-+16+=+0+
Use quadratic formula
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+9+
+c+=+-16+
+x+=+%28+-9+%2B-+sqrt%28+9%5E2+-+4%2A1%2A%28-16%29+%29%29+%2F+%282%2A1%29+
+x+=+%28+-9+%2B-+sqrt%28+81+%2B+64+%29%29+%2F+2+
+x+=+%28+-9+%2B-+sqrt%28+145+%29%29+%2F+2+
+x+=+%28+-9+%2B+12.042+%29+%2F+2+
+x+=+3.042+%2F+2+
+x+=+1.521+
I don't think you can use the negative square root of +145+
at all because you end up with logs of negative numbers,
and that is impossible.
check answer:
+log%28+6%2C%28+1.521%2B5+%29+%29+%2B+log%28+6%2C%28+1.521+%2B+4+%29+%29+=+2+
+log%28+6%2C+6.521+%29+%2B+log%28+6%2C+5.521+%29+=+2+
+1.048+%2B+.96+=+2+
Pretty close