Matematika

Pertanyaan

Jika 2 log 3 = a dan 3 log 5 = b, maka 4 log 45 = ....

2 Jawaban

  • 4 log 45 = 4 log 9 + 4 log 5
    = 2^2 log 3^2 + 2^2 log 5
    = 2 log 3 + 1/2 (2 log 5)
    = a + 1/2 (ab)
    = a (1 + 1/2 b)
  • 2log3 = a dan 3log5 = b
    4log45 = (3log45) / (3log4)
    = (3log3.3.5) / (3log2^2)
    = (3log3 + 3log3 + 3log5) / (2 . 3log2)
    = (1 + 1 + b)/(2 . 1/a)
    = a(2 + b) / 2

    = 1/2 a (b + 2)

    = 1/2 ab + a

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