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Article #13628

Re: about log

#13628
From: HASHIZUME Hiromichi
Date: Tue, 20 Aug 1996 00:00
46 lines
1977 bytes
$B66D^(B@$B3X=Q>pJs%;%s%?!<$H$$$$$^$9!#(B

In article <32190D30.1E1B@micros.co.jp>, Sayaka Yokoi <yokoi@micros.co.jp> writes:
 > $B>pJs=hM};n83$NLdBj$G!"(Blog$B$,$G$F$-$^$7$?!#(B
 >$B!!!!(Blog2$B#1#0#0#0(B=$B#9!%#9#6#5#7(B....  
 > $BE83+$7$F$b(B
 >$B!!!!(Blog2$B#1#0#0#0(B=$B#3(Blog2$B#1#0$G9T$-5M$^$C$F$7$^$$$^$9!#(B
 > $B$3$N@h$I$&$9$l$P$h$$$G$9$+!)$h$m$7$/$*4j$$$7$^$9!#(B

$B8N!&9b66=(=S@h@8$,%(%C%;%$$G=q$$$F$*$i$l$??tCM2r@O$N;n83LdBj(B
$B$NN`Ld$G$"$k2DG=@-$,$"$j$^$9!#(B

$B9b66@h@8$N$b$N$O(B($B<j7W;;$G(B) log10 $B#2(B = 0.3010$B!D(B $B$rM-8z?tCM(B
5$B7e(B($B$@$C$?$+$J(B) $B$G5a$a$h!"$H$$$&$b$N$G!"(BLog10$B#e(B = 0.43429
$B$,%R%s%H$H$7$FDs<($5$l$F$$$k$b$N$G$7$?!#(B

$B>e5-$NLdBj(B (log2 1000 = 9.96$B!D(B $B$r5a$a$h!"$H$$$&$3$H$G$9$h$M(B)
$B$KF1$8<j$,;H$($k$+$I$&$+$OITL@$G$9$,!"$$$A$*$&$=$NJ}K!$rI_^'(B
$B$9$k$H!D(B

ln x $B$O<+A3BP?t$r!"(B lg x $B$O(B2$B$rDl$H$9$kBP?t$rI=$9$b$N$H(B
$B$7$^$9!#(B

$B$?$^$?$^(B 2^10 = 1024 $B$,(B 1000 $B$KHs>o$K6a$$$3$H$rMxMQ$7$^$9!#(B
$B$D$^$j(B 

  lg 1000 = lg(1024 - 24) = lg(1024(1-24/1024))
          = lg1024 + lg(1 - 0.0234375)

$B$3$3$G(B              2    3    4
                   x    x    x
  ln(1-x) = -( x + -- + -- + -- + $B!D(B ) 
                   2    3    4
$B$G$"$k$+$i!"(B

  lg 1000 = 10 - (0.0234375 + 0.0234375^2/2 + $B!D(B)/ln 2

$B$3$3$G$b$7LdBj$N%R%s%H$K(B ln 2 = 0.693 $B$,M?$($i$l$F$$$l$P!"(B
$B#2<!$N9`$^$G$H$C$F(B

  lg 1000 = 9.96578$B!D(B

$B$,F@$i$l$^$9!#(B

 -- $B66D^(B
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Message-ID: <HAS.96Aug20131557@dragon.rd.nacsis.ac.jp>
Path: arc1-ca.pugleaf.net!unknown!not-for-mail
References: <32190D30.1E1B@micros.co.jp>

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X-Google-Language: Japanese,JIS
X-Google-Thread: f4956,e1f496da5335a471
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From: has@rd.nacsis.ac.jp (HASHIZUME Hiromichi)
Subject: Re: about log
Date: 1996/08/20
Message-ID: <HAS.96Aug20131557@dragon.rd.nacsis.ac.jp>
X-Deja-AN: 175376983
references: <32190D30.1E1B@micros.co.jp>
organization: NACSIS, Japan.
newsgroups: fj.sci.math