Matematika

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Ada yang ngerti nomor 4 dan 5?? Tolong dong
Ada yang ngerti nomor 4 dan 5?? Tolong dong

1 Jawaban

  • ^ pangkat
    4) 16^x.16¹ - (2²)^x.2^4 = 32
    16.(4²)^x - 4^x.16 = 32
    16.(4^x)² - 16(4^x) = 32
    misalkan 4^x = p
    16p² - 16p = 32
    16p² - 16p - 32 = 0
    --------------------------- ÷ 16
    p² - p - 2 = 0
    (p - 2)(p + 1) = 0
    p = 2 ----> 4^x = 2
    p = -1 ----> 4^x = -1 (tidak memenuhi karena pankat hasilnya tidak negatif)

    4^(x - 3) = 4^x . 4^-3
    = 2 . 1/4^3
    = 2/64
    = 1/32

    5) 6^x.6² + 6¹.6^-x = 30
    6^x.36 + 6.(1/6^x) = 30
    36.6^x + 6/6^x = 30
    misal 6^x = p
    36p + 6/p = 30
    ---------------------- × p
    36p² + 6 = 30p
    36p² - 30p + 6 = 0
    -------------------------- ÷ 6
    6p² - 5p + 1 = 0
    (3p - 1)(2p - 1) = 0
    3p = 1
    p = 1/3
    6^x = 1/3
    x1 = ^6log 1/3
    2p = 1
    p = 1/2
    6^x = 1/2
    x2 = ^6log 1/2
    x1 + x2 = ^6log 1/3 + ^6log 1/2
    = ^6log (1/3×1/2)
    = ^6log (1/6)
    = ^6log 6^-1
    = -1.^6log 6
    = -1