ΠΛΗ30 ΜΑΘΗΜΑ 1.2
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ΠΛΗ30 ΜΑΘΗΜΑ 1.2
Transcript of ΠΛΗ30 ΜΑΘΗΜΑ 1.2
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30 1:
1.2:
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.
.
1.
1.
2.
3.
4. f(x)=log x
2 , 30, 1.2:
4. f(x)=log x
5.
.
1.
2.
.
.
-
.
:
.
3 , 30, 1.2:
.
(-)
(-)
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. 1. 1.
4 , 30, 1.2:
a b, b a.
b a.
log xbx a b a= =
logb a b a.
:3
24
33
52 2
1/4 2
log 8 3 2 8log 81 4 3 81log 125 3 5 125
1 1 1log 1 /16 24 4 16
= =
= =
= =
= = =
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. 1. 2.
5 , 30, 1.2:
30, , 2,
:
:
X logX
2log logx x=
X logXX logX
1 log1=0
2 log2=1
4 log4=2
8 log8=3
16 log16=4
32 log32=5
64 log64=6
1024 log1024=10
X logX
2048 log2048=11
4096 log4096=12
8192 log8192=13
220 log220=20
230 log230=30
240 log240=40
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. 1. 3. ( )
6 , 30, 1.2:
:
.
:
log logKb ba K a=
:
:
.
: :
(log )Xb a
log Xb a
log loglog (log )
Kb bX Xb b
a K a
a a
=
=
log loglog (log )
K
X X
a K aa a
=
=
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. 1. 3. ( )
7 , 30, 1.2:
,
, :
logloglog
cb
c
aa
b=
2. :
28
2
64
39
3
log 32 5log 32 1.66log 8 3
log 2048 11log 2048 1.83log 64 6
log 27 3log 27 1.5log 9 2
= = =
= = =
= = =
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. 1. 3. ( )
8 , 30, 1.2:
:
log ( ) log log
log log log
b b b
b b b
xy x yx
x yy
= +
=
:
.
:
:
log( ) log log
log log log
xy x yx
x yy
= +
=
log (log )b bxy x y= log log ( )b bxy xy
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. 1. 3. ( )
9 , 30, 1.2:
( )
:
logb xb x=
25
10
log 2
log ( )
510
n
n n
n
n n+
=
= +
,
2. :
22 log
log 4 log 4 2
2
4 2 2 2n
n
n n n
n =
= = =
10log ( )10 n n n n+ = +
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. 1. 4. f(x)=log x
10 , 30, 1.2:
30 ( )
f(x)=log x:
: f(x) ( ).
.
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. 1. 5.
11 , 30, 1.2:
:
:
1
2
( ) log log( ) log log log
f n nf n n
=
=
:
.. :
:
1
2
( ) log(log )( ) log(log(log ))
f n nf n n
=
=
log(log 256) log(8) 3log(log(log16)) log(log 4) log(2) 1
= =
= = =
log log log log log logn n n<
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. 1.
12 , 30, 1.2:
b 2
log xbx a b a= =log 2xx a a= =
log ( ) log logb b bxy x y= + log( ) log logxy x y= +
x x
log log logb b bx
x yy
= log log logx x yy
=
logloglog
cb
c
aa
b=
logloglog 2
c
c
aa =
log logKb ba K a= log logKa K a=log (log )X Xb ba a= log (log )X Xa a=
logb xb x= log2 x x=
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. 2. :
5-6 .
:
13 , 30, 1.2:
:
1. (.) . 1. (
) , 2
2. 2,
3. ( )
4.
log2 xx =
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. 2. 1. (.) (.) .
(.) : .
14 , 30, 1.2:
.
.
.
.
! (.) . : , !
, (.), (.) .
-
. 2. 1. (.) :
15 , 30, 1.2:
/ , (.)
-
. 2. 2. 2
(.)
(! (.) ) 2. :
16 , 30, 1.2:
-
. 2. 3.
.
17 , 30, 1.2:
-
. 2. 4.
,
.
.
!!! ( / , :
18 , 30, 1.2:
/ , :
,
:
. .:
,
. ..:
, ! .
5 6 logn n n n< 1 n
n
1
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. 2. 4.
:
20 , 30, 1.2:
:
:
23log log 2.32n n n
