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:)

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) (Show Source): You can put this solution on YOUR website!
1. Show that log(base 1/c)x = log(base c)1/x
--------------
log(base 1/c)x = m --> (1/c)^m = x --> 1/(c^m) = x --> c^(-m) = x
----
log(base c)1/x = n --> c^n = 1/x --> c^(-n) = x
----------------------
c^-n = x
c^-m = x
------
m = n
log(base 1/c)x = log(base c)1/x
QED

RELATED QUESTIONS
1. Show that log(base 1/c)x = log(base c)1/x Can you please help me out? Thanks so... (answered by lynnlo)

1. Show that log(base 1/c)x = log(base c)1/x Can you please help me out? Thanks so... (answered by Alan3354)

Show that log(base 1/c)x = log(base c)1/x Can you please help me out with this... (answered by josmiceli)

1.Show that log(base c) x/y = -log(base c) 4/x Can you please help me out? Thanks so... (answered by Alan3354)

1. Show that log(base c)x/y = -log(base c)4/x Can you please help me out? Thanks so much (answered by Alan3354)

1. Show that a) log(base 1/c)x = -log(base c)x b) log(base c)1/x = log(1/c)x Can you (answered by Alan3354)

Show that a) log(base 1/c)x = -log(base c)x b) log(base c)1/x = log(1/c)x Can you... (answered by Alan3354)

1. Solve the following equations a) log(base 5)x+2 + log(base 5) x-2 - log(base 5)4 =... (answered by mananth)

Show that log(base c)x/y = -log(base c)4/x Can you please help me out with this... (answered by Alan3354)