diketahui 2 log 3=a , 2 log5=b, nilai 20 log 54 adalah

Kelas 10 Matematika
Bab Logaritma

^ = pangkat

^20log 54
= (²log 54)/(²log 20)
= (²log (27 . 2))/(²log (5 . 4))
= (²log 27 + ²log 2)/(²log 5 + ²log 4)
= (²log 3^3 + 1)/(b + ²log 2²)
= (3a + 1)/(b + 2)

20 log 54 = (4x5) log ( 2x3x3x3)
Gunakan sifat :
a log b = n log b/n log a
20 log 54 = 2 log 54/2 log 20
= 2 log (2x3 ^3)/2 log (2^2x5)
= (2 log 2 + 3. 2 log 3)/(2. 2 log 2 + 2 log 5)
= (1 + 3a)/(2 + b)