sederhanakan 1. 2log 16 + 3log 27 + 5log 1/625 2. 3log 27 + 5log 1/25 - log 0,0001 3. 7log 5. 5 log 6 6log 49 4. 7log 1/49 7log 3 3 log 5 5. 4log 9 . 3log 125 . 25log 16 6. 1/2log 9 . 1/3log 7 . 49log 32 7. 2log 3 . 3log 5 . 5log 6 . 6log 8
1. sederhanakan 1. 2log 16 + 3log 27 + 5log 1/625 2. 3log 27 + 5log 1/25 - log 0,0001 3. 7log 5. 5 log 6 6log 49 4. 7log 1/49 7log 3 3 log 5 5. 4log 9 . 3log 125 . 25log 16 6. 1/2log 9 . 1/3log 7 . 49log 32 7. 2log 3 . 3log 5 . 5log 6 . 6log 8
1. 2log 16 + 3log 27 + 5log 1/625 = 4 + 3 + (-4) = 3.
2. 3log 27 + 5log 1/25 - log 0,0001 = 3 + (-2) - (4) = -3.
3. 7log 5. 5 log 6. 6log 49 = 7log 49 = 2.
4. 7log 1/49 .7log 3. 3 log 5 = 7log 1/49 . 7log 5 = -2. 7log 5
5. 4log 9 .3log 125 . 25 log 16 = 4log3² . 3log 5³. 5²log 4² = 2(4log 3). 2(3log5) . 5log4 = 4(4log4) = 4(1) =4.
6. 1/2log 9 . 1/3log 7 . 49log 32 =
7. 2log 3 . 3log 5 . 5log 6 . 6log 8 = 2log 8 = 3.
2. ^3log 5x^√5log 9+^8log 2/ ^2log 12-^2 log 3
Jawaban:
[tex] = log_{3}(5) \times log_{ \sqrt{5} }(9) + \frac{log_{8}(2)}{log_{2}(12) - log_{2}(3) } \\ = log_{3}(5) \times log_{ {5}^{ \frac{1}{2} } }( {3}^{2} ) + \frac{3}{ log_{2}( \frac{12}{3} ) } \\ = log_{3}(5) \times \frac{2}{ \frac{1}{2} } log_{5}(3) + \frac{3}{ log_{2}(4) } \\ = 4 log_{3}(5) \times log_{5}(3) + \frac{3}{2} \\ = 4 \times 1 + \frac{3}{2} \\ = \frac{11}{2} \\ = 5 \frac{1}{2} [/tex]
3. Sederhanakan nilai tersebut 4log 2 + 4log 8 = 3log 162 - 3log 3= 2log 5 + 2log 8 - 2log 10= 3log 9 + 5log 1/125 - log 0,001= 2log akar 8 + log akar 2 - 2log akar 16=
[tex]^{4}log\ 2\ +\ ^{4}log\ 8\ = ^{4}log\ 2\ .\ 8\ =\ ^{4}log\ 16\ = 2\\\\^{3}log\ 162\ -\ ^{3}log\ 3=\ ^{3}log \frac{162}{3} =\ ^{3}log 54[/tex]
4. Tentukan hasil log dibawah ini 1. a. ^2log 8 + ^2log 4 b. ^6log 4 + ^6log 9 c. ^5log 50 + ^5log 1/2 d. log 125 + log 8 e. ^3log 27 + ^3 log 1/3 f. ^3log 81 - ^3log 27 Tolong beserta caranya yaa:) Terimakasih
a. ²log 8+²log 4 = ²log 2³+²log 2² = (3x²log 2)+(2x²log2) = 3+2 =5
b. 6 log 4 + 6 log 9 = 6 log (4x9) = 6 log 36 = 6 log 6² = 2x 6log 6 = 2
c. 5 log 50 + 5 log 1/2 = 5 log (50/2) = 5 log 25 = 5 log 5² = 2
d. log 125 + log 8 = log (125x8) = log 1000 = log 10³ =3
e. ³log 27 + ³ log 1/3 = ³log (27/3) = ³log 9 = ³log 3² = 2
f. ³log 81 - ³log 27 = ³log 3^4 - ³log 3³ = 4-3 =1
5. (2log 3 + 4log 9)(3log 4 +9 'log 2) =
Jawab:
sifat logaritma;
ᵃlog b = ᵃⁿlogbⁿ
ᵃlog b + ᵃlog c = ᵃlog ( bc)
ᵃlogb x ᵇlogc = ᵃlogc
ᵃlogaⁿ = n
Penjelasan dengan langkah-langkah:
( ²log 3 + ⁴log 9 ) ( ³log 4 + ⁹log 2 )
( ²log 3 + ²log3 ) ( ⁹log 16 + ⁹log 2 )
²log ( 3 x 3 ) ⁹log ( 16 x 2 )
²log 9 x ⁹log 32
²log 32
²log2⁵
5
semoga bisa membantu
6. ^8log 2-^6log 216+^3log 81-^5log 625^1/2
= ⁸ log 2 - ⁶ log 216 + ³ log 81 - ⁵ log 625^¹/₂
= 1/3 - 3 + 4 - ⁵ log 25
= 1 1/3 - 2
= - 2/3
[tex] 8_{log2}- 6_{log216}+ 3_{log81}- 5_{log 625^{ -\frac{1}{2} } } \\ = 2^{3} _{log2}- 6_{log 6^{3} + 3_{log 3^{4} }- 5_{log (5^{ 4)^{ \frac{1}{2} } } } \\ \\ = \frac{1}{3}- 3+4- 5_{log 5^{2} } \\ = \frac{1}{3}- 3+4 -2 \\ = \frac{1-9+12-6}{3} \\ = -\frac{2}{3} [/tex]
7. 1.6 log 2 x 2log 5 x 5log 36 ??? 2. 1per2 log 2 +4log 16 - 3log 9 ??? 3. akar 3 log 9 + 3 log 81 ??? 4. 3log 1per9 - 3log 1per27 ??? 5. log 24 +log 1per2 - log12 ?? 6. log akar20 - log 4 + log akar 2 ??? kak bantuin ..
1. 6'log2 . 2'log5 . 5'log36
= 6'log36
= 2
2. (1/2)' log 2 + 4'log16 - 3'log9
= -2 + 2 - 2
= -2
3. (V3)' log 9 + 3' log 81
= 4 + 4
= 8
4. 3' log (1/9) - 3' log (1/27)
= -2 - (-3)
= -2 + 3
= 1
5. log24 + log(1/2) - log12
= log (24 /(2 . 12))
= log 1
= 0
8. Sederhanakanlah: 1. 2log 4 + 2log 82. 5log ½ + 5log 503. 7log 217 − 7log 314. log 25 – 3 log 5 + log 205. 2^2log 4^3Tolongin dongg...
1. 2log 4 + 2log 8 = 2log 4.8
= 2log 32 = 5
2. 5log ½ + 5log 50 = 5log ½×50
= 5log 25 = 2
3.7log 217 – 7log 31 = 7log 217/31
= 7log 7 = 1
4.log 25 + log 20 - 3log 5
= log 25×20 – 3log 5
= log 500 – 3log 5
5. 2²log 4³ = 2² log (2²)³ = 2² log 2^6 = 3
9. Tolong bantu jawab! 1.Nyatakan ⅓ "log x-5 "log z sebagai suatu logaritma tunggal. 2.Jika a=6log 5 dan b=5log 4,tentukan nilai 4log 0,24 dalam a dan b.
•
(1/3) . ²log x - 5 . ²log z
= ²log x^1/3 - ²log z^5
= ²log (³√x /z^5)
^ baca pangkat
••
6'log 5 = a
5'log 4 = b
4'log 0,24
= 5'log 0,24 / 5'log 4
= 5'log (24/100) / 5'log 4
= 5'log (6/5²) / 5'log 4
= (5'log 6 - 5'log 5²) / 5'log 4
= (1/a - 2) /b
= (1 - 2a) / (ab)
10. hitung penyelesaian dari setiap pertidaksamaan logaritma berikut : a. 7log x > 2 b.3log(2x-7)≤ 3 c. 5log(3x+7)> 3log 16 d. 2log (4x-5) ≤ 2log(x+7) e.4log(x2-2x-8)≥ 2 f. log(x2+3x-10)≥log (x-2) g.6log (4x-3) + 6log x < 0 h.1/3log (2x-1) > -3 Tolong dituliskan caranya ya terimakasih^^
ini yang ku tau... yang c aku gk ngerti...
#semoga bermanfaat
11. bisa bantuin sama caranya . a. 2log 8 + 2log 32 b. log 16 + log25 - log 4 c. 2log 7. 7log 4. 4log 8 d. 3. 3log2 + 2 3log 3 - 3log 3 - 3log 24
a.2log8 = 3.
2log32 = 5
jadi 3+ 5=8
a. 2 log 8 + 2 log 32 = 2 log 8x32 (alog b+alogc = alog bxc)
= 2 log 256
= 2 log 16²
= 2x 2 log 16 ( 2 log 16 = 4)
jadi = 2x4 = 8
b. log 16 + log 25 - log 4 = log 16x25/4
= log 100
= log 10²
= 2x log 10
= 2 ( karena log 10 =1 )
12. sederhanakanlah:a. ²log 50+²log8-²log 100[tex]2log \: \sqrt{8 } + 2log \: \sqrt{2} - 2log \: - 2log \: 16[/tex]c. ²log 16 + 3log 7 x 5log 1/625d. ½log 9 x ⅓log 7 x 49log 32e. 4log 9 x 3log 125 x 25 log 16f. 3log 27 + 5log 1/25 - log 0,0001tolong bantuu kaaaa:(
semoga membantu
semangat terus belajar nya kawan
itu yg b soalnya gk jelas
13. 1. 4log 162. log 10.0003. 5log 1/54. 7log 75. 9log 36. 4log ½
1. . 4log 16=4log4^2=2. 4log4=2
2. log 10.000=log10^3=3
3. 5log 1/5=5log5^-1=-1.5log5=-1
4. 7log 7=1
14. Bantu aku ya guys;;) 1). 2log 50+ 2log 8 - 2log 100? 2). 2log √8 + 2log √2 - 2log 16? 3). 2log 16+ 3log 27 + 5log 1/625? 4). 1/2log 9 x 1/3log 7 x 49 log 32? 5). 4log x log 125 x 25 log 16? 6). 3log 27 + 5log 1/5 - 10log 0,0001? please,help guyyys;'(
1. 2log( 50*8/100)
= 2log (400/100)
=2 log 4
=2 maaf kalo salahno 4.
=2^-1log 3^2 × 3^-1log 7 × 7^2 log 2^5
=-2 × 2log3 × -1 × 3log7 × 5/2 × 7log2
= -5
15. nilai dari 3log 4 . 4log 5 . 5log 6 . 6log 7 . 7log 8 . 8log 9 adalah... (ket: angka pertama sblm log dlm bentuk pangkat)
Tinggal dicoret ajah toh, inget inget lagi sifat log
Hasilnya 3log9 = 2
16. 1.Nyatakan ⅓ "log x-5 "log z sebagai suatu logaritma tunggal. 2.Jika a=6log 5 dan b=5log 4,tentukan nilai 4log 0,24 dalam a dan b.
1. log [(X-5)^1/3 x Z]
2. 4 log 0,24
=5log 0,24/5log 4
=5 log (6 x 4 x 10^-2)/5log 4
=5log 6 + 5log 4+ -2 x 5log 10 / 5log 4
= 1/a + b + -2 x (5 log 5+ 5 log 2) / b
= 1/a + b + -2 (1+b/2) / b
= 1/a + b -2 -b / b
= 1/a - 2 /b
= 1-2a/ab
a = 6log 5
1/a = 5log 6
b = 5 log 2^2
b/2 = 5 log 2
17. Diketahui 2log 3 = x , 5log 2 = y dan 7log 2 = z. Nyatakan dengan x ,y dan z bentuk-bentuk berikut a). 8log 9 b). 5log 15 c). 2log 45d). 18log 20 e). 30log 90 f). 6log 98
LOgaritma
ᵃlog b = ⁿlog b/ ⁿlog a
²log 3 = x
⁵log 2 = y
⁷log 2 = z
dalam bentuk x, y, z berikut
a. ⁸log 9 = ²^³log 3²
= ²/₃ ²log 3
= ²/₃ x
b. ⁵log 15 = ⁵log 3 . ⁵log 5
= ⁵log 2.²log 3. ⁵log 5
= (y)(x)( 1)
= xy
c. ²log 45 = ²log 3² + ²log 5
= 2. ²log 3 + ²log 5
= 2. ²log 3 + 1/(⁵log 2)
= 2(x) + 1/y
= 2x + 1/y
d. ¹⁸log 20 = ⁵log 20 / ⁵log 18
[tex]\sf = \dfrac{^5log2^2 + ^5log 5}{^5log 2 + ^5log 3^2}[/tex]
[tex]\sf = \dfrac{2. ^5log2 + ^5log 5}{^5log 2 + 2. ^5log 3}[/tex]
[tex]\sf = \dfrac{2. ^5log2 + ^5log 5}{^5log 2 + 2. ^5log 2. ^2log 3}[/tex]
[tex]\sf = \dfrac{2y+1}{y+ 2 xy}[/tex]
e. ³⁰log 90 =
[tex]\sf \dfrac{^5log 90}{^5log 30}[/tex]
[tex]\sf \dfrac{^5log 2 + ^5log 3^2 + ^5log 5}{^5log 2 + ^5log 3 + ^5log 5}[/tex]
[tex]\sf \dfrac{^5log 2 +2. ^5log 2. ^2log 3+ ^5log 5}{^5log 2 + ^5log 2. ^2log 3 + ^5log 5}[/tex]
[tex]\sf \dfrac{y +2. y . x+ 1}{y + yx+ 1}[/tex]
[tex]\sf= \dfrac{y +2xy+ 1}{y + xy+ 1}[/tex]
f. ⁶log 98 =
[tex]\sf = \dfrac{^7log 98}{^7 log 6}[/tex]
[tex]\sf = \dfrac{^7log 2.+ ^7log 7^2}{^7 log2+ ^7log 3}[/tex]
[tex]\sf = \dfrac{^7log 2 + 2. ^7log 7}{^7 log2+ ^7log 2. ^2log 3}[/tex]
[tex]\sf = \dfrac{z+ 2 (1)}{z+ (z)(x)}[/tex]
[tex]\sf = \dfrac{z+ 2}{z+ xz}[/tex]
18. 3log 5. √5 log 9 + 8log.2 =2 log 12 - 2log 3
Penjelasan dengan langkah-langkah:
^ artinya pangkat
1] ³log 5 . ^√5log 9 + ^8log 2
= ³log 9 . ^√5log 5 + ^(2³)log 2
= ³log 3² . ^(5^(1/2))log 5 + 1/3 . ²log 2
= 2 . ³log 3 . 1/(1/2) . ^5log 5 + 1/3
= 2 . 2 + 1/3
= 4 1/3
2] ²log 12 - ²log 3
= ²log (12 : 3)
= ²log 4
= ²log 2²
= 2 . ²log 2
= 2
Detail Jawaban
Kelas 10
Mapel 2 - Matematika
Bab 1.1 - Bentuk Akar, Eksponen dan Logaritma
Kode Kategorisasi : 10.2.1.1
19. 2^3log 1/9 + 4log 2 : 9log 2 * 2log 3 =
the log bro ngerti ra we aku wes qatam
20. 1. hitunglah a. 3log [tex] 9^{2} [/tex] b. log 2 + log 10 - log [tex] \frac{1}{5} [/tex] c. 2log 2+2log 3-2log 6-2log 8 2. sederhanakan bentuk logaritma berikut a. 2log 25×3log 8×5log 9
Nomor 1
a)
= ³ log 9²
= ³ log (3² )²
= ³ log 3⁴
= 4 x ³ log 3
= 4 x 1
= 4
b)
= log 2 + log 10 - log 1/5
= log ( 2 x 10 : 1/5 )
= log ( 20 x 5/1 )
= log 100
= log 10²
= 2 x log 10
= 2 x 1
= 2
c)
= ² log 2 + ²log 3 - ² log 6 - ² log 8
= ² log ( 2 x 3 : 6 : 8 )
= ² log ( 6 : 48 )
= ² log (1 / 8 )
= ² log 2⁻³
= -3 x ² log 2
= -3
Nomor 2
a)
= ² log 25 x ³ log 8 x ⁵ log 9
= ² log 5² x ³ log 2³ x ⁵ log 3²
= 2 x ²log 5 x 3 x ³ log 2 x 2 x ⁵ log 3
= (2 x 3 x 2) x ²log 5 x ⁵ log 3 x ³ log 2
= 12 x ² log 3 x ³ log 2
= 12 x ² log 2
= 12
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