SOLUTION: Please help to solve this by hand, much appreciated and thanks a bunch. ln(x/2)-ln(x-1)=ln1

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Please help to solve this by hand, much appreciated and thanks a bunch. ln(x/2)-ln(x-1)=ln1      Log On


   

Question 1021745: Please help to solve this by hand, much appreciated and thanks a bunch.
ln(x/2)-ln(x-1)=ln1
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
log1 = 0. Therefore:
log(x/2)-log(x-1) = 0
log(x/2)-log(x-1) = log(1/(x-1))+log(x/2) = log(x/(2(x-1))):
log(x/(2(x-1))) = 0
Cancel logarithms by taking exp of both sides:
x/(2(x-1)) = 1
Multiply both sides by 2(x-1):
x = 2(x-1)
Expand out terms of the right hand side:
x = 2x-2
Subtract 2x from both sides:
-x = -2
Multiply both sides by -1:
x = 2
Happy learning.
J