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Re: Help with Identities

• To: mathgroup at smc.vnet.net
• Subject: [mg65592] Re: Help with Identities
• From: "david_tang" <david3687 at gmail.com>
• Date: Mon, 10 Apr 2006 02:31:12 -0400 (EDT)
• References: <e1ahdv$2j1$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

dear sir

the reason maybe Mathematica does not know the x and y greater than 0 or not.
so you must assuming the x and y greater than 0;

and more over, the log[] doesn't smarter than man.
so you must tell the Mathematica to do it using the function
FullSimplify or Simplify; and then,
FullSimplify[Log[x/y] == Log[x] - Log[y], x > 0 && y > 0]
NOTE is two == and return true;
but if you use === ans it will return false, because the header is
different i think;

But if you use this
Assuming[x > 0 && y > 0, Log[x/y] === FullSimplify[Log[x] - Log[y]]]
telling the Mathematica the x and y greater than 0 first, you can get
the result true both use == and ===

i hope this will hope you.
you also can test Sin[2 x] == 2 Sin[x] Cos[x];
without Simplify[] you will get nothing.