Logarifm. Logarifmik son
![Logarifm.
Logarifmik son](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_1.png)
![](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_2.png)
![Shotlandiya
matematigi –
logarifmni ixtiro
qilgan
(1550 y - 4 aprel 1617 y .) Джон Непер](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_3.png)
![Logarifm tasnifi
(а >0,a≠1 ) , b a x b
x
a log
8 2 3 8 log
3
2
Misollar](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_4.png)
![Logarifm xossalari 0 1 log 1
a
1 log 2 a
a
y x y x
a a a
log log log 3
y x
y
x
a a a log log log 4
](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_5.png)
![
b
m
b n b
a a
a
n
a
m log
1
log 6
log log 5
b
m
n
b a
n
a m log log 7
x y y x b a b a log log log log ) 8 ](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_6.png)
![ni toping
1
log x = 2 log 5 + log 36 - log 125
7 77 7__ ___
2 31
Yechish :
log x = 2 log 5 + log 6 - log 5
7 77 7
log x = log 5 + log 6
7 77
log x = log 30
7 7
x = 30 Misollar
log 11 – log 44 = log = log =
2 2 2 ____
2____ 11
44 1
42) 1)
-2](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_7.png)
![Lg 2 + lg 5
Log
3 3 – 0,5 log
3 9
Log
2 1/8
Log
4 16 + log
3 27 = 0
= -3
= 5Hisoblang :
=1
Log
8 12 – log
8 15 + log
8 20 =16](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_8.png)
![Xatoni to’g’rilang .](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_9.png)
![Logarifmning qiymatini hisoblang :9 log
3
8
1
log
2
16 log
4
25
1
log
5
3 log 9
1log
7
2 log 32
31
log
3
9 log 27
8log
32
27 log
81
25 log 125
04, 0 log 5
243
1
log 3
100 lg
01, 0 lg
001, 0 lg
9 log
3
09,0log
3,0
3,0
16log
2
2Guruhda ishlash :](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_10.png)
![O’nli logarifm - asosi 10 ni ifodalaydigan
logarifm b b lg log
10
O’nli logarifm xossalari :
n
n
10 lg
n
n
) 1. 0 lg(
n b b
n
lg 10 lg
n b
b
n
lg
10
lg](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_11.png)
![O’nli logarifmlarni hisoblashga doir misollar
lg 1 = , bu yerda 1 = 10 0
lg 10 = 1 , bu yerda 10 = 10 1
lg 100 = 2, bu yerda 100 = 10 2
lg 0,1 = -1, bu yerda 0,1 = 10 -1
lg 0,01 = -2, bu yerda 0,01 = 10 -2
lg 0,001 = -3, bu yerda 0,001 = 10 -30](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_12.png)
![= = = 22
1) Hisoblang
lg8 + lg18_
2 lg2 + lg3 1 = lg (8 18) _
lg (2 3) lg 144 _
lg 12 lg 12
lg 12 ∙ ∙ 10 lg
100 lg
1000 lg
10000 lg
1
2
3
4
1, 0 lg
01, 0 lg
001, 0 lg
0001, 0 lg -1
-2
-3
-4](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_13.png)
![Natural logarifm – asosi е bo’lgan logarifmdir
(е – irratsional son, u taxminan
Ifodalanishi : b b
e
ln log
..., 718281, 2 e (е =2 , 7 ) teng .](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_14.png)
![1) log
4 64= 10) 5 2
•5 log
5 3
=
2) lg 1 = 11) lg 0,1 =
3) log
3 81= 12) l о g
7 7 =
4) log
1/2 16= 13) log
1 2 √ 1 44 =
5) lg 3
√100= 14) log
1/3 1/81=
6) log
1/2 1/32= 15) L о g
5 125 =
7) log
2 3
√2= 16)
1/7 49 =
8) lg 0,001 = 17) log
2 log
3 81=
9) lg 10000= 18) log
2 log
5 625= O’zaki hisoblang
3
0
4
-4
2/3
5
1/3
-3
4 75
-1
1
1/2
4
3
-2
2
2](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_15.png)
![Ko’rsatkichli logarifm :b a
b
a
log
=5; =0,7; =0,4
4 log
4 5
= ; П log
П 2,5
=
2 2 log
2 3
= Ko’rsatkichli funksiyaga asosan :
Yeching :](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_16.png)
![Boshqa asosga o’tish formulasi :
a x
xb
b
a
log log
log
Bu formulaga asoslanib :
a
b
b
a
log
1
log ](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_17.png)
![. 1 log ) 1
3 x
3log)2
61 x
2 log ) 3 5 x
2 log ) 4 7 x
3 log ) 6
21 x
1 log ) 5
7
1 x
0 log ) 6
5
x 3log)5
4 x
4 81 log ) 1 x
2
16
1
log ) 2 x
2
4
1
log ) 3 x
3 27 log ) 4 xMustaqil ishalsh uchun
1- variant 2- variant](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_18.png)
![Javoblari 3
1
) 1 216 ) 2
25 ) 3
49
1
) 4
8 ) 6
7
1
) 5
1 ) 6
64
1
) 5
3) 1
4
1
) 2
2 ) 3 3) 4
1- variant 2- variant](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_19.png)
![Auksion
( kim ko’p ball to’playdi
( uch o’quvchi ) besh baho oladi
1
2
4
06
-1
-3 1/4
3
9
1
1/3
1
5
5 1/9
1/5
1/5 5
1/4
а3)1)
2)
4)
5)
6)
7) 8)
9)
10)
11 )
12 )
13)
14)
15) 16)
17)
18)
20)
21)
22)](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_20.png)
![Masalan : Tenglikni logarifmlaymiz :
, log
1/2 logarifmdan
Potensirlaganimizda :
log
2 8 = 3 , 2 3
= 8 ni hosil qilamiz Ta’rif :-Biror ifodaning logarifmini toppish logarifmlash
deyiladi
Ta’rif Logarifmdan ifoda yoki sonni topish potensirlash
deyiladi](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_21.png)
![1) log
5 25 = 5, bu yerda 5∙5 =
25Xatoni toping
2) log
4 (1/16) = 2, bu yerda 4 2
= 1 /16
3) log
81 9 = 9 , bu yerda 81 = 9∙9
4) 0,3 2 log 0,3 6
= 0,3 log 0,3 6∙ 2
= 0,3 log 0,3 12
= 12
5) log
10 5 + log
10 2 = log
10 (5 +
2) = log
10 7
6) log
1/3 54 – log
1/3 2 = log
1/3 (54-2) = log
1/3 52](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_22.png)
![log
2 16 = …, bu yerda 2 …
= 16.
log
2 = …, bu yerda 2 …
= .
log
2 1 = …, bu yerda 2 …
= 1.
log
√5 25 = …, bu yerda (√5) …
= 25.
log
… 16 = 4, bu yerda … 4
= 16.
log
2 … = 3, bu yerda 2 3
= …
log
… = -5, bu yerda … -5
= .
2 log 2
5 = …
3 log 3…
= 8.
5 log …4
= 4.
log
3… = -4, bu yerda 3 -4
.Bo’shliqni to’ldiring](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_23.png)
![a
3
1
log a
9
log
a
9
1
log a
3
loga
2log1. 2..
.3.
4.
5.Berilgan logarimni 3 asosli logarifmga
keltiring](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_24.png)
![Manbalar
шаблон: Шумарина Вера Алексеевна, учитель
математики ГКС(К)ОУ С(К)ОШ №11 VIII вида
г.Балашова Саратовской области
skosh11.ucoz.ru/ Для оформления презентации
использован интернет-ресурс : цифра.jpg
•
Кудина Л.В . Государственное бюджетное
профессиональное
образовательное учреждение Свердловской области
«Талицкий
лесотехнический колледж им. Н.И.Кузнецова](/data/documents/42fa8be9-249e-4a23-baaf-e03d15c7e16d/page_25.png)
Logarifm. Logarifmik son
Shotlandiya matematigi – logarifmni ixtiro qilgan (1550 y - 4 aprel 1617 y .) Джон Непер
Logarifm tasnifi (а >0,a≠1 ) , b a x b x a log 8 2 3 8 log 3 2 Misollar
Logarifm xossalari 0 1 log 1 a 1 log 2 a a y x y x a a a log log log 3 y x y x a a a log log log 4