Skorr

Sifat logaritma

Bilangan Matematika · SMA medium

Diketahui 2log⁡3=m{}^{2}\log 3 = m dan 2log⁡5=n{}^{2}\log 5 = n. Nilai 2log⁡90{}^{2}\log 90 adalah ....

  1. A
    2m+2n2m + 2n
  2. B
    1+2m+n1 + 2m + n
    ✓
  3. C
    1+m2+n1 + m^2 + n
  4. D
    2+2m+n2 + 2m + n
  5. E
    2+m2+n2 + m^2 + n

Kunci jawaban

B

Penjelasan singkat

90=2⋅32⋅590 = 2\cdot3^2\cdot5, jadi 2log⁡90=1+2m+n{}^{2}\log 90 = 1 + 2m + n.

(Jawaban dihitung & diverifikasi dengan Python/SymPy.)

90=2⋅32⋅590 = 2\cdot3^2\cdot5. Maka 2log⁡90=2log⁡2+2log⁡32+2log⁡5=1+2 2log⁡3+2log⁡5=1+2m+n{}^{2}\log 90 = {}^{2}\log 2 + {}^{2}\log 3^2 + {}^{2}\log 5 = 1 + 2\,{}^{2}\log 3 + {}^{2}\log 5 = 1 + 2m + n → B.

⚡ Latihan Matematika SMA