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Replies: 27   Last Post: Apr 13, 2000 9:25 PM

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 Ted Alper Posts: 118 Registered: 12/6/04
Posted: Apr 6, 2000 1:05 PM

>I came unstuck eventually when someone cleverly asked for 1.5245^20 (or
>something like that). I argued that this was unfair because it was really 19
>calculations but was howled down.

I'm coming to the discussion a bit late, but if you have your log
estimates memorized, you can do some reasonable approximations
here, too... but that just postpones the crash by one level of complexity.
Also the errors do multiply pretty quickly.

Let me see.... the only ones I remember off the top of my head is
ln(10) is pretty close to 2.3 also ln(3) is 1.099
and log-base-10 of 2 is .30103 (I like the palindrome, so I remembered it.
Also, I know 2^10 is a bit more than 10^3, which nails the relationship
down) ln(2) is a bit less than .7, but I don't remember the exact amount)

can I use those?
1.5245 is around 3/2, so ln(1.5245) must be a bit MORE than .399
times 20 must be about 8.. but what on earth is e^8? ln(10^3) is 6.9
ln(10^4) is 9.2, so it's somewhere in there... I need something with a ln
of 8 - 6.9... well, that sounds like 3 (quite close!)... so 3*1000 = 3000
is my estimate.

Phooey, I undershot by about 50%. Heck, most of the error comes from
replacing 1.5245 by 1.5, once you compound the error to the 20th power...
as an estimate for 1.5^20 I'm only off by around 10%.