SOLUTION: I need to solve this logarithmic equation algebraically please. Round to 3 decimal places. lnx+ln(x+1)=3

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Question 926733: I need to solve this logarithmic equation algebraically please. Round to 3 decimal places. lnx+ln(x+1)=3
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The trick is to express +3+
as a natural log
+3+=+ln%28+e%5E3+%29+
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+ln%28x%29+%2B+ln%28+x%2B1+%29+=+ln%28+e%5E3+%29+
+ln%28+x%2A%28+x%2B1+%29%29+=+ln%28+e%5E3+%29+
Now I can say:
+x%2A%28+x%2B1+%29+=+e%5E3+
+x%5E2+%2B+x+-+e%5E3+=+0+
-----------------------
Use quadratic equation
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+1+
+c+=+-e%5E3+
+x+=+%28+-1+%2B-+sqrt%28+1%5E2+-+4%2A1%2A%28-e%5E3%29+%29%29+%2F+%282%2A1%29+
+x+=+%28+-1+%2B-+sqrt%28+1+%2B+4e%5E3+%29%29+%2F+2+
+x+=+-1%2F2+%2B+%28+sqrt%28+1+%2B+4e%5E3+%29%29+%2F+2+
+x+=+-1%2F2++-+%28+sqrt%28+1+%2B+4e%5E3+%29%29+%2F+2+
Hope I got it

Answer by MathLover1(20850) About Me  (Show Source):