Matematika

Pertanyaan

tentukan himpunan penyelesaian dari tiap persamaan eksponen berikut!
(tolong jawab secepatnya, thx)
tentukan himpunan penyelesaian dari tiap persamaan eksponen berikut! (tolong jawab secepatnya, thx)

2 Jawaban

  • d) 4^(x - 1) - 5(2^x) + 16 = 0
    => 4^x . 4^-1 - 5(2^x) + 16 = 0
    => (2^2)^x . 1/4 - 5 (2^x) + 16 = 0 =====> kali 4
    => (2^x)^2 - 20 (2^x) + 64 = 0 =======> misal a = 2^x
    => a^2 - 20a + 64 = 0
    => (a - 4)(a - 16) = 0
    => a = 4 atau a = 16
    => 2^x = 2^2 atau 2^x = 2^4
    => x = 2 atau x = 4
    HP = {2, 4}

    e) 3^(x + 2) + 9^(x + 1) = 810
    => 3^x . 3^2 + 9^x . 9^1 - 810 = 0
    => 3^x . 9 + (3^2)^x . 9 - 810 = 0 ====> bagi 9
    => 3^x + (3^x)^2 - 90 = 0 ==========> misal a = 3^x
    => a + a^2 - 90 = 0
    => a^2 + a - 90 = 0
    => (a + 10)(a - 9) = 0
    => a = -10 atau a = 9
    => 3^x = -10 atau 3^x = 3^2
    => x = - atau x = 2
    HP = {2}
  • jawaban D..............
    Gambar lampiran jawaban nurhibatulah