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Pertanyaan

fraction numerator open parentheses scriptbase log 10 end scriptbase presuperscript 5 close parentheses squared minus open parentheses scriptbase log 2 end scriptbase presuperscript 5 close parentheses squared over denominator scriptbase log square root of 20 end scriptbase presuperscript 5 end fraction equals ....

  1. 1 half

  2. 1

  3. 2

  4. 4

  5. 5

P. Anggraini

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat kembali sifat bentuk logaritma berikut ini!

log presuperscript straight a open parentheses straight b times straight c close parentheses equals logb presuperscript straight a plus logc presuperscript straight a space log presuperscript straight a open parentheses straight b over straight c close parentheses equals logb presuperscript straight a minus logc presuperscript straight a log presuperscript straight a open parentheses straight b to the power of straight m close parentheses equals straight m open parentheses logb presuperscript straight a close parentheses space space space space space loga presuperscript straight a equals 1

Dengan sifat bentuk logaritma tersebut, didapat perhitungan berikut ini.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses log presuperscript 5 10 close parentheses squared minus open parentheses log presuperscript 5 2 close parentheses squared over denominator log presuperscript 5 square root of 20 end fraction end cell equals cell fraction numerator open parentheses log presuperscript 5 10 close parentheses squared minus open parentheses log presuperscript 5 2 close parentheses squared over denominator log presuperscript 5 2 square root of 5 end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 5 10 close parentheses squared minus open parentheses log presuperscript 5 2 close parentheses squared over denominator log presuperscript 5 2 plus scriptbase log square root of 5 end scriptbase presuperscript 5 end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 5 10 close parentheses squared minus open parentheses log presuperscript 5 2 close parentheses squared over denominator log presuperscript 5 2 plus log presuperscript 5 5 to the power of begin display style 1 half end style end exponent end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 5 10 close parentheses squared minus open parentheses log presuperscript 5 2 close parentheses squared over denominator log presuperscript 5 2 plus begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator open parentheses log presuperscript 5 10 close parentheses squared minus open parentheses log presuperscript 5 2 close parentheses squared over denominator begin display style fraction numerator 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 2 times open parentheses open parentheses log presuperscript 5 10 close parentheses squared minus open parentheses log presuperscript 5 2 close parentheses squared close parentheses over denominator begin display style 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 end style end fraction end cell row blank equals cell fraction numerator 2 times open parentheses open parentheses scriptbase log 10 end scriptbase presuperscript 5 minus scriptbase log 2 end scriptbase presuperscript 5 close parentheses open parentheses scriptbase log 10 end scriptbase presuperscript 5 plus scriptbase log 2 end scriptbase presuperscript 5 close parentheses close parentheses over denominator begin display style 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 end style end fraction end cell row blank equals cell fraction numerator 2 times open parentheses open parentheses log presuperscript 5 open parentheses begin display style 10 over 2 end style close parentheses close parentheses open parentheses log presuperscript 5 open parentheses 10 times 2 close parentheses close parentheses close parentheses over denominator begin display style 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 end style end fraction end cell row blank equals cell fraction numerator 2 times open parentheses 1 scriptbase log 20 end scriptbase presuperscript 5 close parentheses over denominator begin display style 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 end style end fraction end cell row blank equals cell fraction numerator 2 times open parentheses scriptbase log open parentheses 5 times 4 close parentheses end scriptbase presuperscript 5 close parentheses over denominator begin display style 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 end style end fraction end cell row blank equals cell fraction numerator 2 times open parentheses scriptbase log 5 plus log presuperscript 5 4 end scriptbase presuperscript 5 close parentheses over denominator begin display style 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 end style end fraction end cell row blank equals cell fraction numerator 2 times open parentheses 1 plus log presuperscript 5 4 close parentheses over denominator begin display style 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 end style end fraction end cell row blank equals cell fraction numerator 2 times open parentheses 1 plus log presuperscript 5 2 squared close parentheses over denominator begin display style 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 end style end fraction end cell row blank equals cell fraction numerator 2 times open parentheses 1 plus 2 log presuperscript 5 2 close parentheses over denominator begin display style 2 scriptbase log 2 plus 1 end scriptbase presuperscript 5 end style end fraction end cell row blank equals 2 row blank blank blank end table end style

Dengan demikian, hasil dari fraction numerator open parentheses log presuperscript 5 10 close parentheses squared minus open parentheses log presuperscript 5 2 close parentheses squared over denominator log presuperscript 5 square root of 20 end fraction adalah 2.

Oleh karena itu, jawaban yang benar adalah C.

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