SOLUTION: ln(x-1)+ln(x+2)=1

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Question 924629: ln(x-1)+ln(x+2)=1
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+ln%28+x-1+%29+%2B+ln%28+x%2B2+%29+=+1+
+ln%28+%28x-1+%29%2A%28+x%2B2+%29+%29+=+ln%28+e+%29+
+%28+x-1+%29%2A%28+x%2B2+%29+=+e+
+x%5E2+-+x+%2B+2x+-+2+=+e+
+x%5E2+%2B+x+-+%28+2+%2B+e+%29+=+0+
-------------------------
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+1+
+c+=+-2+-e+
---------------
Use quadratic formula
+x+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A1%2A%28-2-e%29+%29%29+%2F+%282%2A1%29+
+x+=+%28-1+%2B-+sqrt%28+1+%2B+8+%2B+4%2Ae+%29%29+%2F+2+
+x+=+%28-1+%2B-+sqrt%28+9+%2B+4%2Ae+%29%29+%2F+2+
+x+=+%28-1+%2B-+sqrt%28+9+%2B+10.8731+%29%29+%2F+2+
+x+=+%28-1+%2B-+sqrt%28++19.8731+%29%29+%2F+2+
+x+=+%28-1+%2B-+4.4579%29+%2F+2+
+x+=+3.4579+%2F+2+
+x+=+1.729+
and
+x+=+%28+-5.4579%29+%2F+2+
+x+=+-2.729+
---------------------
check:
+ln%28+x-1+%29+%2B+ln%28+x%2B2+%29+=+1+
+ln%28+1.729-1+%29+%2B+ln%28+1.729%2B2+%29+=+1+
+ln%28+.729+%29+%2B+ln%28+3.729+%29+=+1+
+-.31608+%2B+1.31614+=+1+
+1.00006+=+1+
close enough
You can check the other root