Hitunglah : a. log 560 c. log 18000 b. log 0,012 d. log 14

Nilai logaritma: a. 2.7481, b. -1.9209, c. 4.2552, d. 1.21915

Pembahasan

Untuk menghitung logaritma dari bilangan-bilangan tersebut, kita dapat menggunakan sifat-sifat logaritma dan kalkulator.

a. log 560 = log (56 * 10) = log 56 + log 10 = log (8 * 7) + 1 = log (2^3 * 7) + 1 = 3 log 2 + log 7 + 1
Menggunakan nilai pendekatan:
log 2 ≈ 0.3010, log 7 ≈ 0.8451
Jadi, log 560 ≈ 3(0.3010) + 0.8451 + 1 = 0.9030 + 0.8451 + 1 = 2.7481

b. log 0,012 = log (12 * 10^-3) = log 12 + log 10^-3 = log (3 * 4) - 3 = log 3 + log (2^2) - 3 = log 3 + 2 log 2 - 3
Menggunakan nilai pendekatan:
log 3 ≈ 0.4771, log 2 ≈ 0.3010
Jadi, log 0,012 ≈ 0.4771 + 2(0.3010) - 3 = 0.4771 + 0.6020 - 3 = 1.0791 - 3 = -1.9209

c. log 18000 = log (18 * 1000) = log (2 * 9 * 1000) = log 2 + log (3^2) + log 10^3 = log 2 + 2 log 3 + 3
Menggunakan nilai pendekatan:
log 2 ≈ 0.3010, log 3 ≈ 0.4771
Jadi, log 18000 ≈ 0.3010 + 2(0.4771) + 3 = 0.3010 + 0.9542 + 3 = 4.2552

d. log 14 akar(1,4) = log (14 * 1,4^0.5) = log (14 * (14/10)^0.5) = log (14 * 14^0.5 * 10^-0.5)
= log (14^1.5 * 10^-0.5) = log (14^1.5) + log (10^-0.5) = 1.5 log 14 - 0.5
= 1.5 log (2 * 7) - 0.5 = 1.5 (log 2 + log 7) - 0.5
Menggunakan nilai pendekatan:
log 2 ≈ 0.3010, log 7 ≈ 0.8451
Jadi, log 14 akar(1,4) ≈ 1.5 (0.3010 + 0.8451) - 0.5 = 1.5 (1.1461) - 0.5 = 1.71915 - 0.5 = 1.21915