Kunci Jawaban Matematika Sukino Kelas X Bab 1 LKS 8 Bag A no 16

Buku Matematika Peminatan Sukino Kelas X
Bab 1 Fungsi, Persamaan, dan Pertidaksamaan Eksponensial
LKS 8
Soal dan Jawaban Matematika Kelas X Sukino
Kunci Jawaban Matematika Sukino

16. Nilai x yang memenuhi pertidaksamaan
³√(2^x√ (4^{x - 13 3}√16^{x + 2}  ))≤ 1/√16^{x 3}√4
adalah...

a. x ≤ 16/13
b. x ≤ 13/16
c. x ≤ 0
d. x ≥ -13/16
e. x ≤ - 16/13

Jawaban : A

³√(2^x√ (4^{x - 13 3}√16^{x + 2}  ))
= ³√(2^x√ (4^{x - 13 3}√2^{4x + 8}  ))
= ³√(2^x√ (2^{2x - 26} 2^{(4x + 8)/3}  ))
= ³√(2^x√ (2^{2x - 26 + (4x + 8)/3}  ))
= ³√(2^x√ (2^{(6x - 78 + 4x + 8)/3}  ))
= ³√(2^x 2^{(6x - 78 + 4x + 8)/6}  )
= ³√(2^{(6x - 78 + 4x + 8 + 6x)/6}  )
= 2^{(6x - 78 + 4x + 8 + 6x)/18} 

1/√16^{x 3}√4
=1/√16^x 2^2/3
=1/√2^4x 2^2/3
=1/√2^{4x + 2/3}
=1/√2^{(12x + 2)/3}
=1/2^{(12x + 2)/6}
=2^{(-12x - 2)/6}

2^{(6x - 78 + 4x + 8 + 6x)/18} ≤ 2^{(-12x - 2)/6}
(6x - 78 + 4x + 8 + 6x)/18 ≤ (-12x - 2)/6
(16x - 70)/18 ≤ (-12x - 2)/6
(16x - 70)/18 ≤ (-36x - 6)/18
16x + 36x - 70 + 6 ≤ 0
52x - 64 ≤ 0
x ≤ 64/52
x ≤ 16/13

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