Matematika

Pertanyaan

jika a log b +b log a = 2 maka hubungan antara a dan b adalah
a. a2 + b2 = 1
b. 2a- b = 0
c. a-b = a+ b
d. 2b = a
e. a-b = 0
tolong caranya makasih

1 Jawaban

  • log b/log a + log a/log b = 2
    (log b*log b) + log a*log a)/loga*logb = 2

    anggap log a = x
    angga log b = y

    (x^2 + y^2 )/xy = 2
    x^2 + y^2 = 2xy
    x^2 -2xy + y^2 = 0
    (x-y)^2 = 0
    x - y = 0
    x = y

    log a = log b
    log a - log b = 0
    log (a/b) = 0
    log (a/b) = log 1

    a/b = 1
    a = b
    a - b = 0




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