Matematika

Pertanyaan

1. jika log 2 = x , log 3 = y , dan log 7 = z , maka =
a) log 12
b) log 42
c) log 63
d) log 98

2. jika ^2 log 3 = a dan ^2 log 5 = b , maka nyatakan ekspresi-ekpresi berikut terhadap a/b =
a) ^4 log 9
b) ^8 log 27
c) ^15 log 100
d) ^2 log 15

1 Jawaban

  • 1. jika log 2 = x , log 3 = y , dan log 7 = z , maka =
    a) log 12
    = log(4x3)
    = log4 + log3
    = log2² + log3
    = 2x + y

    b) log 42
    = log(7 x 3 x 2)
    = log 7 + log3 + log2
    = z + y + x

    c) log 63
    = log(7 x 9)
    = log7 + log3²
    = z + 2y

    d) log 98
    = log(9 x 8)
    = 2y + 3x

    2. jika ^2 log 3 = a dan ^2 log 5 = b , maka nyatakan ekspresi-ekpresi berikut terhadap a/b =

    a) ^4 log 9
    ²log9 / ²log4
    = ²log3² / ²log2²
    = 2a / 2

    b) ^8 log 27
    ^2³log3³
    = (3/3)²log3
    =a

    c) ^15 log 100
    = ²log100 / ²log15
    = ²log(25x4) / ²log(5x3)
    = 2b + 2 / b + a

    d) ^2 log 15
    = b + a

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