Diketahui 2log 3=a dan 3log 5=b. Nilai 6log 45=

Mapel : Matematika
Kelas : X SMA
Bab : Eksponen dan Logaritma

Pembahasan :
6log 45
= (3log 45)/(3 log 6)
= (3log 5 + 3log 3 + 3log 3)/(3log 3 + 3log 2)
= (b + 1 + 1)/[1 + (1/a)]
= (b + 2)/[(a + 1)/a]
= (ab + 2a)/(a + 1)

^2 log 3 = a
^3 log 5 = b

^6 log 45
= (^2 log 45)/(^2 log 6)
= (^2 log (3² . 5))/(^2 log (2 . 3))
= (2 . ^2 log 3 + ^2 log 5)/(^2 log 2 + ^2 log 3)
= (2a + ^2 log 3 . ^3 log 5)/(1 + a)
= (2a + ab)/(1 + a)