Question

Contoh soal logaritma beserta penyelesaiannya ! (butuh 40 soal)

Answer 1

Penjelasan:
log2(8)
= log 8 basis 2

1. 2^log2(8)
= 8

Karena a^loga(N) = N

2. 25^log5(3)
= 5^2(log5(3))
= 3^2
= 9

3. 3^3(log3(2))
= 2^3
= 8

4. log10(100)
<=> 10^x = 100
<=> x = 2

5. log3(1/27)
<=> 3^x = 1/27
<=> x = - 3

6. logx(2) = 3
<=> x^3 = 2
<=> x = akar pangkat 3 dari 2

7. log4(x) = 1/2
<=> 4^1/2 = x
<=> 2 = x

8. 64 = 2^6
<=> log2(64) = 6

9. 1/8 = 2^-3
<=> log2(1/8) = -3

10. 3^x = 4
<=> x = log3(4)

11. 2^(x+1) = 3
<=> x + 1 = log2(3)
<=> x = log2(3) - 1

12. 4^(1-x) = 5
<=> 1-x = log4(5)
<=> x = 1 - log4(5)

13. log3(log2(x)) = 1
<=> log3(y) = 1
<=> y = 3^1
<=> y = 3
log2(x) = 3
<=> x = 2^3
<=> x = 8

14. log2(log3(x)) = 4
<=> log2(y) = 4
<=> y = 2^4
<=> y = 16
log3(x) = 16
<=> x = 3^16

15. log2(log1/3(x)) = -2
<=> log2(y) = -2
<=> y = 1/4
log1/3(x) = 1/4
<=> x = 1/3^1/4
<=> x = akar pangkat 4 dari 1/3

Tulislah dalam bentuk eksponensial
16. log10(0.01) = -2
<=> 10^-2 = 0.01

17. log2(32) = 5
<=> 2^5 = 32

18. log1/2(1/16) = 4
<=> (1/2)^4 = 1/16

19. log3(1/81) = -4
<=> 3^(-4) = 1/81

20. log1/5(125) = -3
<=> (1/5)^(-3) = 125

Hitunglah logaritma di bawah

21. log6(1296)
<=> 6^x = 1296
<=> 6^x = 6^4
<=> x = 4

22. log49(akar pangkat 3 dari 1/7)
= log7^2(7^(-1/3))
<=> 7^2x = 7^(-1/3)
<=> x = -1/6

23. log1/16(akar pangkat 5 dari 64)
= log4^(-2) (4^3/5)
<=> 4^(-2x) = 4^3/5
<=> -2x = 3/5
<=> x = -3/10

24. log3(log2(log2(256))
= log3(log2(2^8)
= log3(log2(8)
= log3(3)
= 1

25. log1/6(log2(5^(log5(64))
= log1/6(log2(64)
= log1/6(log2(2^6)
= log1/6(6)
= log6^-1(6)
= -1

26. 3^(-log3(3))
= 3^((-1)(log3(3))
= 3^-1
= 1/3

27. (2^log2(5))^2
= 5^2
= 25

28. 25^-log5(10)
= 5^2(-1)(log5(10))
= 10^-2
= 1/100

29. 49^1/2log7(1/4))
= 7^2(1/2(log7(1/4)))
= 7^log7(1/4)
= 1/4

30. log3(81/5)
= log3(81) - log3(5)
= 4 - log3(5)

loga(x/y) = loga(x) - loga(y)

31. log4(4 × y)
= log4(4) + log4(y)
= 1 + log4(y)

loga(x × y) = loga(x) + loga(y)

32. log3(60) - log3(4)
= log3(60/4)
= log3(15)
= log3(3 × 5)
= log3(3) + log3(5)
= 1 + log3(5)

33. log5(6^25)
= 25log5(6)

loga(x) = m
<=> a^m = x

a^mn = x^n
<=> loga(x^n) = n × m
<=> loga(x^n) = n × loga(x)

34. log3(81 × 3^2/3)
= log3(3^4 × 3^2/3)
= log3(3^14/3)
= 14/3 × log3(3)
= 14/3 × 1
= 14/3

35. log7(49)
= log7(7^2)
= 2log7(7)
= 2 × 1
= 2

36. log3(729) = 6
<=> 3^6 = 729

37. log10(1/10 akar 10) = -3/2
<=> 10^-3/2 = akar 10 / 100

38. log25(125) = x
<=> log5^2(5^3) = x
<=> 5^2x = 5^3
<=> 2x = 3
<=> x = 3/2

39. log2(x^2 - x - 1) = 0
<=> log2(y) = 0
<=> y = 1

x^2 - x - 1 = 1
<=> x^2 - x - 2 = 0
<=> (x-2)(x+1) = 0
<=> x = 2 atau x = -1

40. 2^(2log2(5) + log2(3))
= 2^(log2(5))2 × 2^log2(3)
= 5^2 × 3
= 25 × 3
= 75