Matematika

Pertanyaan

7log 2 = a, 5log 7 = b, maka 5log 40 jika dinyatakan dengan a dan b adalah ...

2 Jawaban

  • 7log 2 = a
    log 2/ log 7 = a
    log 2 = a log 7

    5log 7 = b
    log 7/ log 5 = b
    log 7 = b log 5

    log 2 = a log 7
    log 2 = ab log 5

    5log40 = log 40/log 5 = log 5 . 2 . 2 . 2 / log 5 = log 5 + 3 . log 2 / log 5 = log 5 + 3 . ab log 5 / log 5 = log 5 (1 + 3ab) / log 5 = 1 + 3ab
  • ⁷log2 = a
    ⁵log7 = b
    b . a = ⁵log7 . ⁷log2
    ab = ⁵log2

    ===============================

    ⁵log40
    = ⁵log(5 . 8)
    = ⁵log5 + ⁵log2³
    = 1 + 3 .⁵log2
    = 1 + 3ab

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