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 744706: 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:)

Answer by Alan3354(69443) 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
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log(base 1/c)x = m --> (1/c)^m = x --> 1/(c^m) = x --> c^(-m) = x
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log(base c)1/x = n --> c^n = 1/x --> c^(-n) = x
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c^-n = x
c^-m = x
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m = n
log(base 1/c)x = log(base c)1/x
QED