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Rob guest
Jan-22-07, 10:02 PM (EST)

"A difficult one:"

 Given that:3^x = 4^y = 12^zProve that:1/z = 1/x + 1/y

alexb
Charter Member
1949 posts
Jan-22-07, 10:47 PM (EST)    1. "RE: A difficult one:"
In response to message #0

 I bet this came from a section dealing with logarithms. JJ guest
Jan-24-07, 05:01 AM (EST)

2. "RE: A difficult one:"
In response to message #1

 ln(3^x) = ln(4^y) = ln(12^z) x*ln(3) = y*ln(4) = z*ln(12)y = z*ln(12)/ln(4)x = z*ln(12)/ln(3)(1/x)+(1/y) = (ln(3)/(z*ln(12))+(ln(4)/(z*ln(12))(1/x)+(1/y) = (ln(3)+ln(4)/(z*ln(12)1/x)+(1/y) = ln(12)/(z*ln(12)1/x)+(1/y) = 1/z

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