SOLUTION: 1. Show that log(base 1/c)x = log(base c)1/x Can you please help me out? Thanks so much in advance:) Can you please show all the steps it would really help me understand:)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1. Show that log(base 1/c)x = log(base c)1/x Can you please help me out? Thanks so much in advance:) Can you please show all the steps it would really help me understand:)      Log On


   

Question 744476: 1. Show that log(base 1/c)x = log(base c)1/x
Can you please help me out? Thanks so much in advance:)
Can you please show all the steps it would really help me understand:)
Found 2 solutions by lynnlo, MathTherapy:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
1. Show that log(base 1/c)x = log(base c)1/x

Can you please help me out? Thanks so much in advance:)
Can you please show all the steps it would really help me understand:)

      log+%281%2Fc%2C+%28x%29%29+=+log+%28c%2C+%281%2Fx%29%29
      Focusing on the left side only, we get:
      log+%28%28x%29%29%2Flog+%28%281%2Fc%29%29+=+log+%28c%2C+%281%2Fx%29%29
    log+%28c%2C+%28x%29%29%2Flog+%28c%2C+%281%2Fc%29%29 = log+%28c%2C+%281%2Fx%29%29  ----- Changing to base c on left side
     log+%28c%2C+%28x%29%29%2F%28-+1%29 = log+%28c%2C+%281%2Fx%29%29  ----- Changing log+%28c%2C+%281%2Fc%29%29 to - 1, as c%5E%28-+1%29+=+1%2Fc
   -+log+%28c%2C+%28x%29%29 = log+%28c%2C+%281%2Fx%29%29
log+%28c%2C+%28x%5E%28-+1%29%29%29 = log+%28c%2C+%281%2Fx%29%29
  highlight%28highlight%28log+%28c%2C+%281%2Fx%29%29%29%29 = highlight%28highlight%28log+%28c%2C+%281%2Fx%29%29%29%29 <==== PROVEN