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Pertanyaan

Nilai dari scriptbase log space 81 times scriptbase log space 125 times end scriptbase presuperscript 3 scriptbase log space 32 end scriptbase presuperscript 5 end scriptbase presuperscript 16 adalah horizontal ellipsis 

  1. 8 

  2. 10 

  3. 15 

  4. 28 

  5. 32 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat kembali sifat logaritma berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a space a end cell equals 1 row cell log presuperscript a to the power of n end presuperscript space b to the power of m end cell equals cell m over n times log presuperscript a space b end cell row cell log presuperscript a space b times log presuperscript b space c times log presuperscript c space d end cell equals cell log presuperscript a space d end cell end table

Misalkan: M adalah scriptbase log space 81 times scriptbase log space 125 times end scriptbase presuperscript 3 scriptbase log space 32 end scriptbase presuperscript 5 end scriptbase presuperscript 16.
Dengan menggunakan sifat di atas, maka nilai dari M adalah

table attributes columnalign right center left columnspacing 0px end attributes row M equals cell scriptbase log space 81 times scriptbase log space 125 times end scriptbase presuperscript 3 scriptbase log space 32 end scriptbase presuperscript 5 end scriptbase presuperscript 16 end cell row blank equals cell scriptbase log space 3 to the power of 4 times scriptbase log space 5 cubed times end scriptbase presuperscript 3 scriptbase log space 2 to the power of 5 end scriptbase presuperscript 5 end scriptbase presuperscript 2 to the power of 4 end presuperscript end cell row blank equals cell 4 over 4 space times space log presuperscript 2 space 3 space times space 3 over 1 space times space log presuperscript 3 space 5 space times space 5 over 1 space times space log presuperscript 5 space 2 end cell row blank equals cell 1 space times space 3 space times space 5 space times space log presuperscript 2 space 3 space times space log presuperscript 3 space 5 space times space log presuperscript 5 space 2 end cell row blank equals cell 15 space times space log presuperscript 2 space 2 end cell row blank equals cell 15 space times space 1 end cell row M equals 15 end table

Jadi, nilai dari scriptbase log space 81 times scriptbase log space 125 times end scriptbase presuperscript 3 scriptbase log space 32 end scriptbase presuperscript 5 end scriptbase presuperscript 16 adalah 15. 

Oleh karena itu, jawaban yang benar adalah C.

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