Log[Exp[x]]
- To: mathgroup at smc.vnet.net
- Subject: [mg5720] Log[Exp[x]]
- From: TTCJ34A at prodigy.com (DR JOHN C ERB)
- Date: Sat, 11 Jan 1997 14:29:12 -0500
- Sender: owner-wri-mathgroup at wolfram.com
>Dear friends, suppose x is a variable and when I type "Log[Exp[x]]" and then >enter, Mathematica gives me "Log[Exp[x]]" back. Could you please tell me how >to let Mathematica to return "Log[Exp[x]]" as x? >Thank you very much. >Cheng Li >chengli at uab.edu NOTE: In: x==Exp[Log[x]] Out: True In: x==Log[Exp[x]] Out: x == Log[Exp[x]] WHY IS THE FIRST EVALUATED TO TRUE, WHILE THE SECOND REMAINS UNEVALUATED? FOR REAL NUMBERS, THE "LOG" AND "EXP" ARE MONOTONIC INVERSES; THERE IS A ONE-TO-ONE CORRESPONDENCE. FOR IMAGINARY NUMBERS, THIS IS NOT TRUE. CONSIDER: In: Exp[Pi I] Out: -1 In: Exp[-Pi I] Out: -1 BOTH OF THESE EVALUATE TO THE SAME VALUE: -1. NOW WHEN WE TAKE THE LOG, WE HAVE: In: Log[-1] Out: I Pi THE LOG[-1] EVALUATES TO (Pi I), BUT BOTH EXP[Pi I] AND EXP[-Pi I] EVALUATE TO -1! SO SINCE MATHEMATICA DOES NOT KNOW IF "X" IS REAL OR IMAGINARY, IT DOES NOT KNOW WHICH WAY TO GO FOR LOG[EXP[X]]. John C. Erb