Soal dan Pembahasan Matematika Sukino Kelas X Bab 1 LKS 5 no 8

Buku Matematika Peminatan Sukino Kelas X
Bab 1 Fungsi, Persamaan, dan Pertidaksamaan Eksponensial
LKS 5
Soal dan Jawaban Matematika Kelas X Sukino


8. Nilai n yang memenuhi persamaan :
1,5ⁿ = 1,2^{n + 3} 
adalah ...

A. 3 (log6 - log5) / (log5 - log4)
B. 3 (log6 + log5) / (log5 - log4)
C. (log6 - log5) / 3(log5 - log4)
D. (log5 - log4) / (log6 - log5)
E. (log5 + log4) / (log6 - log5)

Jawaban : A

1,5ⁿ = 1,2^{n + 3} 
log 1,5ⁿ = log 1,2^{n + 3} 
n log 1,5 = (n + 3) log 1,2
n log (15/10) = (n + 3) log (12/10)
n log (3/2) = (n + 3) log (6/5)
n log (3/2) = n log (6/5) + 3 log(6/5)
n log (3/2) - n log (6/5) = 3 log(6/5)
n (log (3/2) / (6/5) ) = 3 log(6/5)
n (log (3/2) . (5/6) ) = 3 log(6/5)
n log (5/4) = 3 log(6/5)
n = 3 log (6/5) / log (5/4)
n = 3 (log6 - log5) / (log5 - log4)

>>Soal 9