SOLUTION: Solve the equation: ln(x^2 + 1) - ln(x - 1) = 1 + ln (x + 1)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the equation: ln(x^2 + 1) - ln(x - 1) = 1 + ln (x + 1)      Log On


   

Question 1059239: Solve the equation: ln(x^2 + 1) - ln(x - 1) = 1 + ln (x + 1)
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+ln%28+x%5E2+%2B+1+%29+-+ln%28+x+-+1+%29+=+1+%2B+ln%28+x+%2B+1+%29+
+ln%28+%28+x%5E2+%2B+1+%29%2F%28+x+-+1+%29+%29+=+ln%28+e+%29++%2B+ln%28+x+%2B+1+%29+
+ln%28+%28+x%5E2+%2B+1+%29%2F%28+x+-+1+%29+%29+=+ln%28+%28+x+%2B+1+%29%2Ae+%29+
+%28+x%5E2+%2B+1+%29+%2F+%28+x+-+1+%29+=+%28+x+%2B+1+%29%2Ae+
+x%5E2+%2B+1+=+%28+x%5E2+-+1+%29%2Ae+
+%28+e+-+1+%29%2Ax%5E2+=+e+%2B+1+
+x%5E2+=+%28+e+%2B+1+%29+%2F+%28+e+-+1+%29+
+x+=+sqrt%28+%28+e+%2B+1+%29+%2F+%28+e+-+1+%29+%29+
Check my math

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation: ln(x^2 + 1) - ln(x - 1) = 1 + ln (x + 1) ]
----------------------
ln[(x^2+1)/((x-1)(x+1))] = 1
-----------------------
(x^2+1)/(x^2-1) = e
---------------
x^2 + 1 = e*x^2 - e
---
(1-e)x^2 = -(e+1)
x^2 = (-e-1)/(-e+1)
x^2 = 2.1640
x = 1.471
------------
Cheers,
Stan H.
-----------