Latihan Soal Matematika Peminatan Kelas X 2019
Fungsi, Persamaan, dan Pertidaksamaan Eksponensial
Fungsi, Persamaan, dan Pertidaksamaan Logaritma
Vektor
40. Diketahui bahwa (x,y,z) memenuhi persamaan :
2 log [3 log (4 log x)] = 3 log [4 log (2 log y) ] = 4 log [2 log ( 3 log z)] = 0
Tentukan nilai dari x - 2y - z
Jawaban :
2 log [3 log (4 log x)] = 3 log [4 log (2 log y) ] = 4 log [2 log ( 3 log z)] = 0
2 log [3 log (4 log x)] = 2 log 1
3 log (4 log x) = 1
3 log (4 log x) = 3 log 3
4 log x = 3
4 log x = 4 log 43
x = 43 = 64
3 log [4 log (2 log y) ] = 0
3 log [4 log (2 log y) ] = 3 log 1
4 log (2 log y) = 1
4 log (2 log y) = 4 log 4
2 log y = 4
2 log y = 2 log 24
y = 24 = 16
4 log [2 log ( 3 log z)] = 0
4 log [2 log ( 3 log z)] = 4 log 1
2 log ( 3 log z) = 1
2 log ( 3 log z) = 2 log 2
3 log z = 2
3 log z = 3 log 32
z = 32 = 9
x - 2y - z
= 64 - 2 . 16 - 9
= 64 - 32 - 9
= 23
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