Matematika

Pertanyaan

Tolong dibantu ya kakak tentang logaritma prnya buat besok
Pakek caranya
Kalo bener & dijawab semua aku kasih yang terbaik deh
Tolong dibantu ya kakak tentang logaritma prnya buat besok Pakek caranya Kalo bener &  dijawab semua aku kasih yang terbaik deh

1 Jawaban

  • a)
    ²log x + ²log (x - 2) = 3
    ²log [x(x - 2)] = ²log2³
    ²log [x(x - 2)] = ²log8

    x(x - 2) = 8
    x² - 2x - 8 = 0
    (x + 2)(x - 4) = 0

    x + 2 = 0
    x = -2 (tidak memenuhi)

    x - 4 = 0
    x = 4 (memenuhi)

    HP = {4}

    b)
    log(x - 2) + log (x  - 1) = log 6
    log [(x-2)(x-1)] = log 6
    log(x² - 3x + 2) = log 6

    x² - 3x + 2 = 6
    x² - 3x + 2 - 6 = 0
    x² - 3x - 4 = 0
    (x + 1)(x - 4) = 0

    x + 1 = 0
    x = -1 (tidak memenuhi)

    x - 4 = 0
    x = 4

    HP = {4}

    c)
    log (2x - 1) - log (x - 3) = log 7
    log [(2x - 1) / (x - 3)] = log 7

    (2x - 1) / (x - 3) = 7
    2x - 1 = 7(x - 3)
    2x - 1 = 7x - 21
    2x - 7x = -21 + 1
    -5x = -20
    x = 4

    HP = {4}