SOLUTION: Solve the equation log(x+1)-log(x+2)=log(1/x)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the equation log(x+1)-log(x+2)=log(1/x)      Log On


   

Question 377744: Solve the equation
log(x+1)-log(x+2)=log(1/x)
Found 2 solutions by robertb, stanbon:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The equation becomes:
log%28%28x%2B1%29%2F%28x%2B2%29%29+=+log%281%2Fx%29;
%28x%2B1%29%2F%28x%2B2%29+=+1%2Fx, since log is a one-to-one function.
x(x+1) = x+2, after cross-multiplication.
x%5E2+%2B+x+=+x%2B2,or
x%5E2+=+2, or x+=+-sqrt%282%29 or x+=+sqrt%282%29. The first value will NOT satisfy the original equation, and so the final answer is x+=+sqrt%282%29.

Answer by stanbon(75887) About Me  (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.