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Re: Log function

• To: mathgroup at smc.vnet.net
• Subject: [mg57349] Re: Log function
• From: Jean-Marc Gulliet <jeanmarc.gulliet at 9online.fr>
• Date: Wed, 25 May 2005 06:02:57 -0400 (EDT)
• Organization: New York University
• References: <d6us3g$j02$1@smc.vnet.net>
• Reply-to: jmg336 at nyu.edu
• Sender: owner-wri-mathgroup at wolfram.com

Bill Ginsberg wrote:
> I have Mathematica 5.0.1.  When I attempt to get the Log of a number "a" 
> by entering Log[a], it does not return the value but echoes back: 
> Log[a].  How is this fixed?

Hi Bill,

I will assume that by "a" you mean any positive real value, say for 
example two. You can enter the value two as an exact number, for 
instance 2 without any decimal point (unlimited precision, not dependent 
of the hardware) or as a machine-precision number (limited number of 
digit after the decimal point, dependent on which the hardware 
architecture is used), for instance 2. or 2.0

What does that change in our case for the value of the logarithm? If you 
enter an exact number, Mathematica will work in exact arithmetic and 
give you exact number. The exact value of Log[2] is Log[2] since Log[2] 
is an irrational number that is it has an unlimited non-repetitive 
series of numbers after the decimal point (such as Pi or e, base of the 
natural logarithms). Hence

In[1]:= Log[2]

Out[1]= Log[2]

Also

In[2]:= Log[1]

Out[2]= 0

To get an approximate value you can either type in a decimal point or 
use the function N (for Numerical I think):

In[3]:= Log[2.]

Out[3]= 0.693147

In[4]:= Log[2]//N

Out[4]= 0.693147

In[5]:= N[Log[2],20]

Out[5]= 0.69314718055994530942

Best regards,
/J.M.