Rumus atau Definisi Logaritma (Log) Beserta Contoh Soal dan Jawaban

Definisi Logaritma 

Contoh soal dan jawaban logaritma (log)  :

1. ²log 24 + ²log 3 -  ²log 9 =
2.  log 5 + log 4 -  log 2 + log 10 =
3. ³log 27 =
4. log (x² + 4x + 4) < log (5x +10) =
5. Jika ²log 3 = p dan ²log5 = q maka ²log 45 adalah  =
6. Jika ²log3 = m dan ²log5 = n maka ²log 135 adalah =

Jawab

1. ²log 24  + ²log 3 - ²log 9 = 

²log (24 * 3)/9 = ²log 72/9 = ²log 8 = 3

 

 2. log 5 + log 4 -  log 2 + log 10 =

 log (5 * 4 * 10)/2 = log (200)/2 = log 100 = 2

 

  3. ³log 27 = 

³log 3³ = 3 * ³log 3  = 3 * 1 = 3

 

 4. x² + 4x + 4 < 5x +10 = 

x² + 4x - 5x + 4 - 10 < 0 = x² + (-x) - 6 < 0 = (x - 3)(x - 2)< 0 = -2 < x <3

 

5. ²log 45 = 

²log(3² x 5) = ²log3² + ²log5 = 2²log3 + ²log5 = 2p + q

 

 6. ²log 135 = 

²log 27  ²log 5 = ²log 3 ²log 9 ²log 5 = ²log 3 m n = 2 m²n

Contoh soal Logaritma  :