Hasil 3log 36 − 3log 43log 25 × 5log 81 + 4log 2​ adalah ...

Pertanyaan

Hasil fraction numerator log presuperscript 3 space 25 space cross times space log presuperscript 5 space 81 space plus space log presuperscript 4 space 2 over denominator log presuperscript 3 space 36 space minus space log presuperscript 3 space 4 end fraction adalah ...

  1. 13 over 4

  2. 17 over 4

  3. 9 over 2

  4. 13 over 2

  5. 17 over 2

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Ingat sifat-sifat logaritma:

  1. log presuperscript straight a space straight a equals 1
  2. log presuperscript straight a space straight a to the power of straight m equals straight m
  3. log presuperscript straight a to the power of straight n end presuperscript space straight b to the power of straight m equals straight m over straight n times log presuperscript straight a space straight b
  4. 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
  5. log presuperscript straight a space straight b cross times log presuperscript straight b space straight c equals log presuperscript straight a space straight c


Maka diperoleh:


begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator log presuperscript 3 space 25 cross times log presuperscript 5 space 81 space plus space log presuperscript 4 space 2 over denominator log presuperscript 3 space 36 space minus space log presuperscript 3 space 4 end fraction end cell equals cell fraction numerator log presuperscript 3 space 5 squared cross times log presuperscript 5 space 3 to the power of 4 plus log presuperscript 2 squared end presuperscript space 2 over denominator log presuperscript 3 space begin display style 36 over 4 end style end fraction end cell row blank equals cell fraction numerator 2 cross times log presuperscript 3 space 5 cross times 4 cross times log presuperscript 5 space 3 plus begin display style 1 half end style log presuperscript 2 space 2 over denominator log presuperscript 3 space 9 end fraction end cell row blank equals cell fraction numerator 8 cross times log presuperscript 3 space 5 cross times log presuperscript 5 space 3 plus begin display style 1 half end style over denominator log presuperscript 3 space 3 squared end fraction end cell row blank equals cell fraction numerator 8 times log presuperscript 3 space 3 plus begin display style 1 half end style over denominator 2 times log presuperscript 3 space 3 end fraction end cell row blank equals cell fraction numerator 8 plus begin display style 1 half end style over denominator 2 end fraction end cell row blank equals cell 17 over 4 end cell end table end style


Oleh karena itu, jawaban yang benar adalah B.

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