SOLUTION: Show that log(base 1/c)x = log(base c)1/x Can you please help me out with this question? Thanks so much in advance:) Can you show all the steps because it will help me unders

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


   

Question 744755: Show that log(base 1/c)x = log(base c)1/x

Can you please help me out with this question? Thanks so much in advance:)
Can you show all the steps because it will help me understand more thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Prove:
+log%28+1%2Fc%2C+%28x%29+%29+=+log%28+c%2C+%281%2Fx%29+%29+
I will say that
+a+=++log%28+1%2Fc%2C+%28x%29+%29+
+b+=+log%28+c%2C+%281%2Fx%29+%29+
Now I can say
(1) +%28+1%2Fc+%29%5Ea+=+x+
(2) +c%5Eb+=+1%2Fx+
-----------------
(2) +1%2F%28+c%5Eb+%29+=+x+
Now I can say
+1%2F%28+c%5Eb%29+=+%28+1%2Fc%29%5Ea+
This is the same as
+%28+1%2Fc+%29%5Eb+=+%28+1%2Fc+%29%5Ea+
+a+=+b+
+log%28+1%2Fc%2C+x+%29+=+log%28+c%2C+1%2Fx+%29+