SOLUTION: ln(1/x)+lnx=0 I have no idea if this one is right. I have to see if it is true or false. Do you know? Thank you.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: ln(1/x)+lnx=0 I have no idea if this one is right. I have to see if it is true or false. Do you know? Thank you.      Log On


   



Question 33577: ln(1/x)+lnx=0 I have no idea if this one is right. I have to see if it is true or false. Do you know? Thank you.
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!

ln(1/x) + lnx = 0

          lnx = -ln(1/x)

Replace 1/x by x-1

          lnx = -ln(x-1)

Use rule lnBA = AlnB

          lnx = -(-1)lnx

          lnx = lnx

Thus this is an identity for all values of x
for which lnx is defined.  lnx is defined for
all positive x, so the solution set is

       {x|x > 0} or (0, ¥)

Edwin
AnlytcPhil@aol.com