Nilai x jika log(x) – log(3) = 5
1. Nilai x jika log(x) – log(3) = 5
LogAritMa
log x – log 3 = 5
log (x/3) = log 10^5
x/3 = 10^5
x = 3 . 10^5
x = 300000
2. Log(x-3)+ log(x-5) = 1 maka nilai x adalah
[tex] \begin{align} \log (x-3) + \log (x – 5) &= 1 \\ \log ((x – 3)(x – 5)) &= \log 1 \\ \log (x^2 – 8x + 15) &= \log 1 \\ x^2 – 8x + 15 &= 1 \\ x^2 – 8x + 14 &= 0 \\ x &= \frac{8 \pm \sqrt{64 – 56}}{2} \\ x &= 4 \pm \sqrt{2} \end{align} [/tex]
3. tent nilai x dari log(x-3)+log(x+1)= log 5
jawabannya 4 cara ada di gambar
4. tent nilai x dari log(x-3)+log(x+1)= log 5
log ((x-3)(x+1))= log 5
(x-3)(x+1)=5
x^2+x-3x-3 =5
x^2 -2x -3-5 =0
x^2 -2x -8 =0
(x-4) (x+2) =0
x= 4 atau x =-2
5. nilai sederhana dari 2 log 3 x 3 log 5 x 5 log 6 x 6 log 8
2 log 8 = 2 log 2³ = 3
sisanya log 3 x 3 log 5 x 5 log 6 x 6 ini dicoret semua
Jadi sisa 2 log 8
Penjelasan dengan langkah-langkah:
²log 3 × ³log 5 × ⁵log 6 × ⁶log 8
= ²log 8
= ²log 2³
= 3
6. tent nilai x dari A. log(x-3)+log(x+1)= log 5B. log (x+1)-log(x-1)= log 3
itu jawabannya ya
a. 4
b. 2
cara di gambar
7. Bilangan Logaritma ○tentukan nilai X,jika nilai X bilangan real : 1. log 3 + log 4 = log 9x 2. log (x+1) – log
(x-1) = log 3 3. log (x-3) + log (x+1) = log 5 4. log (x+6) = log x +log 3
1. log (3 × 4) = log 9x
log 12 = log 9x
maka: 12 = 9x
x = 12/9
2. log (x+1) – log (x-1) = log 3
log [(x+1) / (x-1)] = log 3
maka:
x + 1 / x – 1 = 3
x + 1 = 3 (x – 1)
x + 1 = 3x – 3
x – 3x = -3 – 1
– 2x = -4
x = 2
Untuk nomor 3 dan 4 coba dikerjakan sendiri berdasarakan ulasan di atas 🙂
semoga bermanfaat
8. nilai x yang memenuhi 5 log (x + 5)+5 log(x-3)-5 log(x+15)=0
5’log (x + 5) + 5’log (x – 3) – 5’log (x + 15) = 0
5’log (x + 5)(x – 3)/(x + 15) = 5’log 1
(x + 5)(x – 3)/(x + 15) = 1
Kalikan silang
(x + 5)(x – 3) = x + 15
x² + 2x – x – 15 – 15 = 0
x² + x – 30 = 0
(x – 5)(x + 6) = 0
x = 5 atau x = -6
syarat numerus : > 0
nilai x yg memenuhi :
x = 5Bab Logaritma
Matematika SMA Kelas X
⁵log (x + 5) + ⁵log (x – 3) – ⁵log (x + 15) = 0
⁵log ((x + 5) . (x – 3) /(x + 15)) = 0
(x + 5) . (x – 3) / (x + 15) = 5⁰
(x + 5) . (x – 3) = 1 . (x + 15)
x² + 2x – 15 = x + 15
x² + 2x – 15 – x – 15 = 0
x² + x – 30 = 0
(x + 6) (x – 5) = 0
x + 6 = 0
x = -6 (tidak memenuhi karena negatif)
x – 5 = 0
x = 5 (memenuhi karena positif)
HP = { 5 }
pembuktian
⁵log (5 + 5) + ⁵log (5 – 3) – ⁵log (5 + 15) = ⁵log 10 + ⁵log 2 – ⁵log 20
= ⁵log (10 x 2 : 20)
= ⁵log 1
= 0
terbukti
9. Tentukan nilai x2 log 5 x = 3 log x
Jawab:
x = 25
Penjelasan dengan langkah-langkah:
2log 5x = 3log x
[tex]log (5x)^{2}[/tex] = [tex]log x^{3}[/tex]
[tex](5x)^{2}[/tex] = [tex]x^{3}[/tex]
[tex]x^{3} – 25x^{2}[/tex] = 0
[tex]x^{2} (x – 25)[/tex] = 0
syarat yang harus dipenuhi adalah x ≠ 0
maka yang memenuhi adalah x – 25 = 0
x = 25
10. nilai x yang memenuhi 5^log(x-1) = 1 – 5^log(x+3) adalah
.
5’log(x-1) = 5’log 5 – 5’log (x+3)
5’log(x-1) = 5’log (5/(x+3))
syarat pembatas
x-1 > 0 –> x > 1
x+3 ≠ 0 n x+3 > 0
(x.>1) n (x>-3)—> x > 1
(x-1) = 5/(x+3)
(x-1)(x-+3) = 5
x²+ 2x -3 -5 = 0
x² + 2x -8 = 0
(x+4)(x-2) = 0
x= -4 (TM) krne x > 1
x = 2[tex]$\begin{align} ^5\log(x-1)&=1-{^5}\log(x+3)\\^5\log(x-1)&={^5}\log5-{^5}\log(x+3)\\^5\log(x-1)&={^5}\log\frac{5}{x+3}\\x-1&=\frac{5}{x+3}\\5&=(x-1)(x+3)\\5&=x^2+2x-3\\0&=x^2+2x-8\\x&=(x+4)(x-2)\\x&=\boxed{-4\ $atau$\ 2} \end[/tex]
11. tentukan nilai X jika 5 log (x + 1)+5 log (x + 3)-1
Jawaban:
5 log (x+6)/x = 5 log 5
(x+6)/x = 5
x+6 = 5x
4x = 6
x = 3/2
Penjelasan dengan langkah-langkah:
maaf kalu salah
12. carilah nilai xdarilog(2x-3)-log(x-3) = log 5
Jawab:
x = 4
Penjelasan dengan langkah-langkah:
log (2x – 3) – log (x – 3) = log 5
log (2x – 3)/(x – 3) = log 5
(2x – 3)/(x – 3) = 5
2x – 3 = 5x – 15
2x – 5x = -15 + 3
-3x = -12
x = 4
13. 3 5^log 2 +⅔ 5^log 8-5^log 3=5^log xnilai x adalah…
5^log 2^3 +5^log 8^(2/3)-5^log3=5^logx
5^loh8+5^log4-5^log3=5^logx
5^log (8×4:3)=5^logx
32/3=x
14. Jika log x + 2 log x^2 + 3 log x^3 = 3 log 6^3 + 5 log 3 – log 4, maka nilai x adalah
log x + 2 log x^2 + 3 log x^3 = 3 log 6^3 + 5 log 3 – log 4
Log x + Log (x²)² + Log (x³)³ = Log(6³)³ + Log3^5 – Log2²
Log x.x^4.x^9 = Log (6^9.3^5)/2²
Log x^14 = Log(2^9.3^9.3^5)/2²
14Logx = Log(2^7.3^14)
Log x = (1/14)Log(2^7.3^14)
Log x = Log (2^7.3^14)^(1/14)
x = (2^7.3^14)^(1/14)
= 2^(1/2)(3)
= 3√2
15. Nilai x yang memenuhi log x^5 – 3 log x + log x + log 1/x² = 1 adalah…….
[tex]l0ogx^5-3logx+logx+log \frac{1}{x^2}=1 \\ logx^5-3logx+logx+log x^{-2}=1 \\ 5logx-3logx+logx-2logx=1 \\ (5-3+1-2)logx=1 \\ logx=1 \\ 10^1=x \\ 10=x[/tex]log x^5 – 3 log x + log x + log 1/x² = 1 .
5 log x – 3 log x + log x + log x⁻² = 1 .
5 log x – 3 log x + log x + -2 log x = 1 .
(5-3+1-2) log x = 1
log x = 1
log x = log 10
x = 10
16. Jika log x + 2 log x^2 + 3 log x^3 = 3 log 6^3 + 5 log 3 – log 4, maka nilai x adalah
logx+logx^4+logx^9=log6^9+log3^5-log4
logx^14=log(6^9)(3^5):(2^2)
x^14=(6^9)(3^5):(2^2)
x^14=(2^9).(3^9).(3^5):(2^2)
x^14=(2^7).(3^14)
pangkat14nya di keluarin
x^14=((2^0,5).(3^1))^14
x=(2^0,5).(3^1)
x=√2.3
x=3√2
maaf kalau salah
Pembahasan:
[tex]log x+2log x^{2} +3log x^{3} =3log 6^{3} +5log3-log4 \\ logx+log(x^{2})^{2} +log(x^{3})^{3} =log (6^{3})^3 +log3^{5}-log4 \\ logx.x^{4}.x^{9}=log \frac{6^9.3^5}{4} =logx^{14}=log \frac{2^2.3^2.6^7.3^5}{2^2} \\ logx^{14}=log6^7.3^7 \\ logx^{14}=log18^7 \\ x^{14}=18^7 \\ x= \sqrt[14]{18^7} \\ x= 18^{ \frac{7}{14} } \\ x= 18^{ \frac{1}{2} } \\ x= \sqrt{18} \\ x= \sqrt{9.2} \\ x=3 \sqrt{2} [/tex]
Sekian penjelasan dariku, semoga membantu 🙂 jangan lupa, jadikan yang terbaik ya :p
17. Nilai x dari 5^x log 8-3/5-^x log 8 =6
5^xlog8-3/5-^xlog8=6
Misal: ^xlog8=a
5a-3/5-a=6
5a-3=30-6a
11a=33
a=33/11=3
^xlog8=a
^xlog8=3
^xlog2^3=3
3.^xlog2=3
^xlog2=3/3=1
x=2
18. Tentukan nilai x yang memenuhi : a.) Log (x + 1) – Log (x – 1) = log 3 b.) 5 log (x + 1) + 5 log(x – 3) = 5 log 5
Semoga bermanfaat, terima kasihA. Log (x + 1) – Log (x – 1) = log 3
Sesuai sifat logaritma log a – log b = log a/b
Maka
Log (x + 1) – Log (x – 1) = log 3
Log (x+1)/(x-1) = log 3
(x+1)/(x-1) = 3
x+1 = 3x-3
-2x = -4
x = 2
B. 5 log (x + 1) + 5 log(x – 3) = 5 log 5
Sesuai sifat logaritma log a + log b = log ab
Maka
5 log (x + 1) + 5 log(x – 3) = 5 log 5
5 log (x+1)(x-3) = 5 log 5
(x+1)(x-3) = 5
x² – 2x – 3 = 5
x² – 2x – 8 = 0
( x – 4 ) ( x + 2 ) = 0
x – 4 = 0
x = 4
Dan
x + 2 = 0
x = -2
Semoga jelas ya kak
19. Tentukan nilai x! log x^5 – 3 log x^2 + log x^4 + log√x^3 = 9
log x^5 – 3 log x^2 + log x^4 + log √x^3 = 9
5 . log x – 2 . 3 . log x + 4 . log x + 3/2 . log x = 9
5 . l
og x – 6 . log x + 4 . log x + 3/2 . log x = 9
log x . (5 – 6 + 4 + 3/2) = 9
log x . 9/2 = 9
log x = 9 : 9/2
log x = 9 . 2/9
log x = 2
10^2 = x
x = 100
