Tentukan nilai logaritma berikut. b. log 10+log 2−log 4+log 20

Pertanyaan

Tentukan nilai logaritma berikut.

b. log space 10 plus log space 2 minus log space 4 plus log space 20

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

diperoleh nilai table attributes columnalign right center left columnspacing 0px end attributes row cell log space 10 plus log space 2 minus log space 4 plus log space 20 end cell equals 2 end table.

Pembahasan

Ingat sifat-sifat logaritma berikut:

  • log presuperscript straight a space straight b plus log presuperscript straight a space straight c equals log presuperscript straight a space straight b times straight c
  • log presuperscript straight a space straight b minus log presuperscript straight a space straight c equals log presuperscript straight a space straight b over straight c
  • table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript straight a space straight a to the power of straight n end cell equals cell straight n times log presuperscript straight a space straight a end cell row blank equals cell straight n times 1 end cell row blank equals straight n end table

Jika basis tidak ditulis, nilainya adalah 10. Berdasarkan sifat tersebut, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell log space 10 plus log space 2 minus log space 4 plus log space 20 end cell equals cell log space fraction numerator 10 times 2 times 20 over denominator 4 end fraction end cell row blank equals cell log space 400 over 4 end cell row blank equals cell log space 100 end cell row blank equals cell log space 10 squared end cell row blank equals 2 end table

Jadi, diperoleh nilai table attributes columnalign right center left columnspacing 0px end attributes row cell log space 10 plus log space 2 minus log space 4 plus log space 20 end cell equals 2 end table.

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