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Pertanyaan

Jika begin mathsize 14px style log presuperscript p space a equals 2 end style dan begin mathsize 14px style log presuperscript q space 8 p equals 2 end style, maka begin mathsize 14px style log presuperscript 2 p end presuperscript space fraction numerator p q squared over denominator a end fraction equals... end style 

  1. begin mathsize 14px style 3 space log presuperscript 2 space 2 p end style 

  2. begin mathsize 14px style log presuperscript 2 space 2 p end style 

  3. begin mathsize 14px style fraction numerator 3 over denominator 2 space log space 2 p end fraction end style 

  4. begin mathsize 14px style fraction numerator 1 over denominator 2 space log space 2 p end fraction end style 

  5. begin mathsize 14px style fraction numerator 3 over denominator 2 space log space p end fraction end style 

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Pembahasan

Berdarkan yang diketahui, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript p space a end cell equals 2 row blank left right double arrow cell fraction numerator log space a over denominator log space p end fraction equals 2 end cell row blank left right double arrow cell log space a equals 2 log space p end cell row blank left right double arrow cell log space a equals log space p squared end cell row blank blank blank row cell log presuperscript q space 8 p end cell equals 2 row blank left right double arrow cell fraction numerator log space 8 p over denominator log space q end fraction equals 2 end cell row blank left right double arrow cell log space 8 p equals 2 log space q end cell row blank left right double arrow cell log space 8 p equals log space q squared end cell end table end style 

Dengan demikian, dengan menggunakan sifat-sifat logaritma maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 p end presuperscript fraction numerator p q squared over denominator a end fraction end cell equals cell log presuperscript 2 p end presuperscript space p q squared minus log presuperscript 2 p end presuperscript space a end cell row blank equals cell fraction numerator log space p q squared minus log space a over denominator log space 2 p end fraction end cell row blank equals cell fraction numerator log space p plus log space q squared minus log space a over denominator log space 2 p end fraction end cell row blank equals cell fraction numerator log space p plus log space 8 p minus log space p squared over denominator log space 2 p end fraction end cell row blank equals cell fraction numerator log open parentheses begin display style fraction numerator p times 8 p over denominator p squared end fraction end style close parentheses over denominator log space 2 p end fraction end cell row blank equals cell fraction numerator log space 8 over denominator log space 2 p end fraction end cell row blank equals cell log presuperscript 2 p end presuperscript space 8 end cell row blank equals cell log presuperscript 2 p end presuperscript space 2 cubed end cell row blank equals cell 3 space log presuperscript 2 p end presuperscript space 2 end cell row blank equals cell 3 open parentheses fraction numerator 1 over denominator log presuperscript 2 space 2 p end fraction close parentheses end cell row blank equals cell fraction numerator 3 over denominator log presuperscript 2 space 2 p end fraction end cell end table end style 

Sehingga, begin mathsize 14px style log presuperscript 2 p end presuperscript space fraction numerator p q squared over denominator a end fraction equals fraction numerator 3 over denominator log presuperscript 2 space 2 p end fraction end style.

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