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Jika log 2=p dan log 3=q, maka nilai dari 2log 12 adalah ...

Pertanyaan

Jika log space 2 equals straight p dan log space 3 equals straight q, maka nilai dari log presuperscript 2 space 12 adalah ...

  1. 2 p and q

  2. p and 2 q

  3. 2 plus p over q

  4. 2 plus q over p

  5. fraction numerator 2 p and q over denominator q end fraction

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingatlah sifat-sifat logaritma yang akan digunakan pada bentuk penyederhanaan berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log space straight b end scriptbase presuperscript straight a end cell equals cell fraction numerator scriptbase log space straight b end scriptbase presuperscript straight p over denominator scriptbase log space straight a end scriptbase presuperscript straight p end fraction end cell row cell scriptbase log space straight b end scriptbase presuperscript straight a straight c end cell equals cell scriptbase log space straight b end scriptbase presuperscript straight a plus scriptbase log space straight c end scriptbase presuperscript straight a end cell row cell log presuperscript straight a space straight b to the power of straight m end cell equals cell straight m space scriptbase log space straight b end scriptbase presuperscript straight a end cell end table

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space 12 end cell equals cell fraction numerator log space 12 over denominator log space 2 end fraction end cell row blank equals cell fraction numerator log space 4 times 3 over denominator log space 2 end fraction end cell row blank equals cell fraction numerator log space 2 squared times 3 over denominator log space 2 end fraction end cell row blank equals cell fraction numerator log space 2 squared plus log space 3 over denominator log space 2 end fraction end cell row blank equals cell fraction numerator 2 times log space 2 plus log space 3 over denominator log space 2 end fraction end cell row blank equals cell fraction numerator 2 straight p plus straight q over denominator straight p end fraction end cell row blank equals cell 2 plus straight q over straight p end cell end table

Maka, nilai dari log presuperscript 2 space 12 adalah 2 plus q over p.

Jadi, jawaban yang tepat adalah D.

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