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Bentuk sederhana dari  adalah ...

Pertanyaan

Bentuk sederhana dari fraction numerator open parentheses log invisible function application x close parentheses squared minus open parentheses log invisible function application y close parentheses squared over denominator scriptbase log invisible function application 4 end scriptbase presuperscript 125 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 9 end scriptbase presuperscript 8 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction adalah ...

  1. 2 over 3 log invisible function application left parenthesis x y right parenthesis

  2. 1 third log invisible function application left parenthesis x y right parenthesis

  3. 3 over 2 log invisible function application left parenthesis x y right parenthesis

  4. log invisible function application left parenthesis x y right parenthesis

  5. 3 log invisible function application left parenthesis x y right parenthesis

Pembahasan:

Untuk menyelesaikan soal tersebut ingat sifat-sifat berikut.

  • scriptbase log invisible function application b to the power of m end scriptbase presuperscript a to the power of n end presuperscript equals m over n times scriptbase log invisible function application b end scriptbase presuperscript a
  • scriptbase log invisible function application b end scriptbase presuperscript a times scriptbase log invisible function application c end scriptbase presuperscript b equals scriptbase log invisible function application c end scriptbase presuperscript a
  • scriptbase log invisible function application a end scriptbase presuperscript a equals 1
  • scriptbase log invisible function application b end scriptbase presuperscript a minus scriptbase log invisible function application c end scriptbase presuperscript a equals scriptbase log invisible function application b over c end scriptbase presuperscript a

Sehingga akan didapatkan

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses log invisible function application x close parentheses squared minus open parentheses log invisible function application y close parentheses squared over denominator scriptbase log invisible function application 4 end scriptbase presuperscript 125 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 9 end scriptbase presuperscript 8 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction end cell equals cell fraction numerator left parenthesis log invisible function application x plus log invisible function application y right parenthesis left parenthesis log invisible function application x minus log invisible function application y right parenthesis over denominator scriptbase log invisible function application 2 squared end scriptbase presuperscript 5 cubed end presuperscript times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 3 squared end scriptbase presuperscript 2 cubed end presuperscript times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 scriptbase log invisible function application 2 end scriptbase presuperscript 5 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus 2 over 3 scriptbase log invisible function application 3 end scriptbase presuperscript 2 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 scriptbase log invisible function application 5 end scriptbase presuperscript 5 times log invisible function application x minus 2 over 3 scriptbase log invisible function application 2 end scriptbase presuperscript 2 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 times 1 times log invisible function application x minus 2 over 3 times 1 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 times log invisible function application x minus 2 over 3 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 left parenthesis log invisible function application x minus log invisible function application y right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 open parentheses log invisible function application open parentheses x over y close parentheses close parentheses end fraction end cell row blank equals cell fraction numerator log invisible function application left parenthesis x y right parenthesis over denominator 2 over 3 end fraction end cell row blank equals cell 3 over 2 log invisible function application left parenthesis x y right parenthesis end cell end table end style

Jadi, dapat disimpulkan bahwa bentuk sederhana dari fraction numerator open parentheses log invisible function application x close parentheses squared minus open parentheses log invisible function application y close parentheses squared over denominator scriptbase log invisible function application 4 end scriptbase presuperscript 125 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 9 end scriptbase presuperscript 8 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction adalah 3 over 2 log invisible function application left parenthesis x y right parenthesis.

Oleh karena itu, jawaban yang benar adalah C.

Jawaban terverifikasi

Dijawab oleh:

M. Iqbal

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 10 Juli 2021

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