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Re: napier and logarithms
From: Dave Walden
Date: 2009 May 28, 10:40 -0700

```A number with 3011 places must be between 1*10**3010 and 10*10**3010.  Or
equivalently, between 10**3010 and 10**3011.  Since this is 2**10,000, let's
take the 10,000th root of both sides.

If lower end of range:

2**10,000 = 10**3010

take the root by dividing the exponents by 10,000:

2**(10,000/10,000)=10**(3010/10,000)

2**1=10**.3010

2=10**.3010

log 2 =.3010

If upper end of range, same method;

log 2 =.3011

So it's somewhere in between.  Why not guess .30105?  In fact, 10**.30105=2.000092126 or so.

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