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Belajar Matematika yuk!

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Belajar Matematika yuk!

Post by Fizan32 on Wed Apr 09, 2008 2:28 pm

Itung2 nih Pelajaran paling asu.......GWe post yg paling pertma...

itung2 ni post kluar kale waktu ntar kelas 3 gwe post yah....

Persamaan Logaritma


Adalah persamaan yang didalamnya terdapat logaritma dimana numerus
ataupun bilangan pokoknya berbentuk suatu fungsi dalam x.

Masalah : Menghilangkan logaritma

alog f(x) = alog g(x) f(x) = g(x)

alog f(x) = b f(x) =ab

f(x)log a = b (f(x))b = a


BATASAN

Logaritma bilangan b dengan bilangan pokok a sama dengan c yang memangkatkan a sehingga menjadi b.

a log b = c ac = b mencari pangkat

Ket : a = bilangan pokok (a > 0 dan a 1)
b = numerus (b > 0)
c = hasil logaritma

Dari pengertian logaritma dapat disimpulkan bahwa :

alog a = 1 ; alog 1 = 0 ; alog an = n

Dengan syarat x yang didapat dari persamaan tersebut harus terdefinisi. (Bilangan pokok > 0 1 dan numerus > 0 )

Contoh:

Tentukan nilai x yang memenuhi persamaan berikut !

1. xlog 1/100 = -1/8
x-1/8 = 10-2
(x -1/Cool -8 = (10-2)-8
x = 10 16

2. xlog 81 - 2 xlog 27 + xlog 9 + 1/2 xlog 729 = 6
xlog 34 - 2 xlog33 + xlog + 1/2 xlog 36 = 6
4 xlog3 - 6 xlog3 + 2 xlog3 + 3 xlog 3 = 6
3 xlog 3 = 6
xlog 3 = 2
x = 3 x = 3 (x>0)

3. xlog (x+12) - 3 xlog4 + 1 = 0
xlog(x+12) - xlog 4 = -1
xlog ((x+12)/4) = -1
(x+12)/4 = 1/x
x + 12x - 64 = 0
(x + 16)(x - 4) = 0
x = -16 (TM) ; x = 4

4. logx - 2 logx - 3 = 0

misal : log x = p

p - 2p - 3 = 0
(p-3)(p+1) = 0

p1 = 3
log x = 3
x1 = 2 = 8

p2 = -1
log x = -1
x2 = 2-1 = 1/2

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Re: Belajar Matematika yuk!

Post by Fizan32 on Wed Apr 09, 2008 2:30 pm

SIFAT-SIFAT

1. alog bc = alogb + alogc
2. alog bc = c alog b
3. alog b/c = alog b -alog c Hubungan alog b/c = - a log b/c
4. alog b = (clog b)/(clog a) Hubungan alog b = 1 / blog a
5. alog b. blog c = a log c
6. a alog b = b
7. alog b = c aplog bp = c Hubungan : aqlog bp = alog bp/q
= p/q alog b

Keterangan:

1. Bila bilangan pokok suatu logaritma tidak diberikan, maka maksudnya logaritma tersebut berbilangan pokok = 10.

[ log 7 maksudnya 10log 7 ]

2. lognx adalah cara penulisan untuk (logx)n
Bedakan dengan log xn = n log x

Contoh:

1. Tentukan batas nilai agar log (5 + 4x - x) dapat diselesaikan !
syarat : numerus > 0
x -4x - 5 < 0
(x-5)(x+1) < 0

-1 < x < 5


2. Sederhanakan

2 3log 1/9 + 4log 2 = 2(-2) + 1/2 =
3log 2. 2log 5 .52log 3 3log 2.2log 5. 5log3

- 3 1/2 = -3 1/2 = -7
3log 31/2 1/2


3. Jika 9log 8 = n Tentukan nilai dari 4log 3 !

9log 8 = n
3log 2 = n
3/2 3log 2 = n
3log 2 = 2n
3

4log 3 = 2log 3
= 1/2 log 3
= 1/2 ( 1/(log 2) )
= 1/2 (3 / 2n)
= 3/4n


4. Jika log (a / b4) Tentukan nilai dari log (b/a) !

log (a/b4)
log (a/b)
2 log ( a/b)
log ( a/b )
log (b/a) = -24
= -24
= -24
= -12
= log (b/a)1/3
= 1/3 log (b / a)
= -1/3 log (a/b)
= -1/3 (-12) = 4]

Bilangan pokok a > 0 1
Tanda pertidaksamaan tetap/berubah tergantung nilai bilangan pokoknya
a > 1

0 < a < 1

a log f(x) > b f(x) > ab
a log f(x) < b f(x) < ab

(tanda tetap)


a log f(x) > b f(x) < ab
a log f(x) < b f(x) > ab

(tanda berubah)
syarat f(x) > 0


Contoh:

Tentukan batas-batas nilai x yang memenuhi persamaan

1. log(x - 2x) < 3
a = 2 (a>1) Hilangkan log Tanda tetap

# - 2 < x < 0 atau 2 < x < 4

1. x - 2x < 2
x - 2x -8 < 0
(x-4)(x+2) < 0
-2 < x < 4

2. syarat : x - 2 > 0
x(x-2) > 0
x < 0 atau x > 2


# 1/2log (x - 3) < 0
a = 1/2 (0 < a < 1) Hilangkan log Tanda berubah


x < - 2 atau x > 2

1. (x - 3) > (1/2)0
x - 4 > 0
(x -2)(x + 2) < 0
x < -2 atau x > 2

2. syarat : x - 3 > 0
(x - 3)(x + 3) > 0
x < 3 atau x > 3



Segini dolo Ntar Pada Pusing lageee........ lol! lol! lol!

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Re: Belajar Matematika yuk!

Post by iKaka' on Wed Apr 09, 2008 2:42 pm

Wah ,, pusink tuh post,, btw, ada yang gagal ya Symbolnya..

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Re: Belajar Matematika yuk!

Post by cegeb on Wed Apr 09, 2008 2:44 pm

1. xlog 1/100 = -1/8
x-1/8 = 10-2
(x -1/Cool -8 = (10-2)-8
x = 10 16

bagian situ salah...

yang bener

1. xlog 1/100 = -1/8
x-1/8 = 10-2
(x -1/ -8 = (10-2)-8
x = 10 16


Last edited by thyanz on Wed Apr 09, 2008 3:40 pm; edited 1 time in total

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Re: Belajar Matematika yuk!

Post by Fizan32 on Wed Apr 09, 2008 3:24 pm

sep2...Ntar GWe betoloin kok......................

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Re: Belajar Matematika yuk!

Post by Fe_dHi on Mon Apr 21, 2008 11:12 am

wah so pinter u zan....................

wae rmed weh MTK............
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