SOLUTION: Solve the equation
log(x+1)-log(x+2)=log(1/x)
Algebra.Com
Question 377744: Solve the equation
log(x+1)-log(x+2)=log(1/x)
Found 2 solutions by robertb, stanbon:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The equation becomes:
;
, since log is a one-to-one function.
x(x+1) = x+2, after cross-multiplication.
,or
, or or . The first value will NOT satisfy the original equation, and so the final answer is .
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
log(x+1)-log(x+2)=log(1/x)
------------
log[(x+1)/(x+2)] = log(1/x)
------
(x+1)/(x+2) = 1/x
-----
x(x+1) = x+2
x^2+x-x-2 = 0
---
x^2-2 = 0
(x-sqrt(2))(x+sqrt(2)) = 0
-------------------
x = sqrt(2)
====================
Cheers,
Stan H.
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