Contoh Soal Logaritma SNMPTN

1. Jika log log x + log 2 = 1, maka nilai ^xlog 5 = …

Jawab:

misalkan,

log x = a

log log x + log 2 = 1

log a + log 2 = 1

log 2.a = log 10

2a = 10

2. log x = 10

log x² = log 10¹⁰

x² = 10¹⁰

x = √10¹⁰

x = 10⁵

maka,

^xlog 5 = ^{10^5}log 5 = 1/5 . ¹⁰log 5 = 1/5 . log 5

2. Jika ⁴log 5 = p dan ⁴log 28 = q, maka ⁴log 70 = ….

Jawab:

⁴log 70 = ⁴log (28 . 5 / 2) = ⁴log 28 + ⁴log 5 - ⁴log 2 = q + p – ^{2^2} log 2 = p + q – ½.

3. Jika a > 1, b > 0 dan c > 1, maka nilai ^blog √a . ^clog b² . ^alog √c = ….

Jawab:

^blog √a . ^clog b² . ^alog √c = ^blog √a .  ^alog √c .  ^clog b² = ^blog a^1/2 .  ^alog c^1/2 .  ^clog b² = ½ . ^blog a . ½ .  ^alog  c . 2.  ^clog b² = 2/4. ^blog a .  ^alog c .  ^clog b = ½ . b log b = ½.

  

Jawab:

5. Jika ⁴log 6 = m + 1, maka ⁹log 8 = …

Jawab:

⁴log 6 = ^{2^2}log 2.3 = ½ (²log 2 + ²log 3) = ½ + ½ . ²log 3 =  m + 1

½ . ²log 3 = m + 1 – ½

²log 3 = 2 ( m + ½ )

²log 3 = 2m + 1

⁹log 8 = 1 / ⁸log 9 = 1/ ^{2^3}log 3² = 1 / 2/3 . ²log 3 = 3 / 2 . ²log 3 = 3 / 2(2m + 1) = 3 / (4m + 2)