Matematika

Pertanyaan

A. 4^{x+1} - 6. 2^{x+1} = -8
B. 2^{2x+1} - 4.2^{x+2} ≤ 0

1 Jawaban

  • a. 4^(x+1) - 6.2^(x+1) = -8
    2^(2x+2) - 6. 2^x. 2 = -8
    2^2x. 2^2 - 12. 2^x= -8
    4. 2^2x -12. 2^x =-8
    misal 2^x = a
    maka
    4a^2 - 12a + 8 = 0
    a = 1 atau a = 2
    maka
    2^x =1 -> x= 0
    2^x = 2 -> x= 1

    b. 2^{2x+1} - 4.2^{x+2} ≤ 0
    2^2x. 2 - 4. 2^x. 2^2
    ≤ 0
    2^2x. 2 - 16 2^x ≤ 0
    misal 2^x= a
    maka
    2a^2 -16a
    ≤ 0
    2a(a - 8)
    ≤ 0
    a
    ≤ 0 atau a-8 ≤ 0
    a
    ≤8 maka
    2^x
    ≤ 8
    x
    ≤ 3

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