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Pertanyaan

Himpunan penyelesaian pertidaksamaan log presuperscript 2 space log presuperscript 2 x greater than log presuperscript 2 left parenthesis 3 minus log presuperscript 2 x right parenthesis plus 1 adalah

  1. open curly brackets x vertical line x greater than 4 close curly brackets

  2. open curly brackets x vertical line 1 less than x less than 8 close curly brackets

  3. open curly brackets x vertical line 4 less than x less than 8 close curly brackets

  4. open curly brackets x vertical line 1 less than x less than 4 close curly brackets

  5. open curly brackets x vertical line x less than 4 close curly brackets

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat pertidaksamaan logaritma dan sifat logaritma

log presuperscript a space f left parenthesis x right parenthesis greater than log presuperscript a space g left parenthesis x right parenthesis rightwards double arrow f left parenthesis x right parenthesis greater than g left parenthesis x right parenthesis scriptbase log space b plus scriptbase log space c plus end scriptbase presuperscript a equals scriptbase log space b c end scriptbase presuperscript a end scriptbase presuperscript a scriptbase log space b minus scriptbase log space c plus end scriptbase presuperscript a equals scriptbase log space b over c end scriptbase presuperscript a end scriptbase presuperscript a

dengan f left parenthesis x right parenthesis comma g left parenthesis x right parenthesis greater or equal than 0 space dan space a greater than 1.

Sehingga bisa dilakukan operasi sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space log presuperscript 2 x end cell greater than cell log presuperscript 2 left parenthesis 3 minus log presuperscript 2 x right parenthesis plus 1 end cell row cell log presuperscript 2 space log presuperscript 2 x end cell greater than cell log presuperscript 2 left parenthesis 3 minus log presuperscript 2 x right parenthesis plus log presuperscript 2 space 2 to the power of 1 end cell row cell log presuperscript 2 space log presuperscript 2 x end cell greater than cell log presuperscript 2 left parenthesis 3 minus log presuperscript 2 x right parenthesis 2 end cell row cell log presuperscript 2 x end cell greater than cell left parenthesis 3 minus log presuperscript 2 x right parenthesis 2 end cell row cell log presuperscript 2 x end cell greater than cell 6 minus 2 log presuperscript 2 x end cell row cell log presuperscript 2 x end cell greater than cell log presuperscript 2 space 2 to the power of 6 minus log presuperscript 2 x squared end cell row cell log presuperscript 2 x end cell greater than cell log presuperscript 2 space 64 over x squared end cell row x greater than cell 64 over x squared end cell row cell x cubed end cell greater than 64 row x greater than 4 end table

Ingat syarat logaritma

table attributes columnalign right center left columnspacing 0px end attributes row x greater than 0 row cell 3 minus log presuperscript 2 space x end cell greater than 0 row 3 greater than cell log presuperscript 2 space x end cell row cell log presuperscript 2 space 2 cubed end cell greater than cell log presuperscript 2 space x end cell row 8 greater than x end table

Jika digabungkan, diperoleh himpunan penyelesaian pertidaksamaan log presuperscript 2 space log presuperscript 2 x greater than log presuperscript 2 left parenthesis 3 minus log presuperscript 2 x right parenthesis plus 1 adalah open curly brackets x vertical line 4 less than x less than 8 close curly brackets.

Oleh karena itu, jawaban yang benar adalah C.

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