Nilai x yang memenuhi pertidaksamaan: 0,1log(x2−1)>2 adalah ...

Pertanyaan

Nilai x yang memenuhi pertidaksamaan: scriptbase log invisible function application left parenthesis x squared minus 1 right parenthesis end scriptbase presuperscript 0 , 1 end presuperscript greater than 2 adalah ...

  1. negative square root of 1 , 01 end root less than x less than square root of 1 , 01 end root

  2. x less than negative square root of 1 , 01 end root atau x greater than square root of 1 , 01 end root

  3. negative 1 less than x less than 1

  4. negative square root of 1 , 01 end root less than x less than negative 1 atau 1 less than x less than square root of 1 , 01 end root

  5. 0 less than x less than square root of 1 , 01 end root

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat pada pertidaksamaan bentuk logaritma jika scriptbase log invisible function application f left parenthesis x right parenthesis end scriptbase presuperscript a greater than scriptbase log invisible function application b end scriptbase presuperscript a dan 0 less than a less than 1 maka 0 less than f open parentheses x close parentheses less than b.

Ingat juga sifat-sifat pada bentuk bentuk logaritma yaitu  

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

Sehingga akan diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application open parentheses x squared minus 1 close parentheses end scriptbase presuperscript 0 , 1 end presuperscript end cell greater than 2 row cell scriptbase log invisible function application left parenthesis x squared minus 1 right parenthesis end scriptbase presuperscript 1 over 10 end presuperscript end cell greater than cell 2 times scriptbase log invisible function application 10 end scriptbase presuperscript 10 end cell row cell scriptbase log invisible function application left parenthesis x squared minus 1 right parenthesis end scriptbase presuperscript 10 to the power of negative 1 end exponent end presuperscript end cell greater than cell scriptbase log invisible function application 10 squared end scriptbase presuperscript 10 end cell row cell negative 1 times scriptbase log invisible function application left parenthesis x squared minus 1 right parenthesis end scriptbase presuperscript 10 end cell greater than cell scriptbase log invisible function application 100 end scriptbase presuperscript 10 end cell row cell scriptbase log invisible function application left parenthesis x squared minus 1 right parenthesis to the power of negative 1 end exponent end scriptbase presuperscript 10 end cell greater than cell scriptbase log invisible function application 100 end scriptbase presuperscript 10 end cell row cell left parenthesis x squared minus 1 right parenthesis to the power of negative 1 end exponent end cell greater than 100 row cell left parenthesis x squared minus 1 right parenthesis to the power of 1 end cell less than cell 100 to the power of negative 1 end exponent end cell row cell x squared minus 1 end cell less than cell 1 over 100 end cell row cell x squared minus 1 end cell less than cell 0 , 01 end cell row cell x squared end cell less than cell 0 , 01 plus 1 end cell row cell x squared end cell less than cell 1 , 01 end cell row x less than cell square root of 1 , 01 end root end cell row x less than cell plus-or-minus square root of 1 , 01 end root end cell end table

Didapatkan x less than square root of 1 , 01 end root atau x greater than negative square root of 1 , 01 end root.

Karena syarat numerus pada bentuk logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu b greater than 0, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 1 end cell greater than 0 row cell x squared end cell greater than 1 row x greater than cell square root of 1 end cell row x greater than cell plus-or-minus 1 end cell end table

Didapatkan x greater than 1 dan x less than negative 1

Dari hasil di atas maka penyelesainnya yaitu irisan dari x less than square root of 1 , 01 end rootx greater than negative square root of 1 , 01 end rootx greater than 1, dan x less than negative 1 yaitu negative square root of 1 , 01 end root less than x less than negative 1 atau 1 less than x less than square root of 1 , 01 end root.

Jadi, dapat disimpulkan bahwa nilai x yang memenuhi pertidaksamaan: scriptbase log invisible function application left parenthesis x squared minus 1 right parenthesis end scriptbase presuperscript 0 , 1 end presuperscript greater than 2 adalah negative square root of 1 , 01 end root less than x less than negative 1 atau 1 less than x less than square root of 1 , 01 end root.

Oleh karena itu, jawaban yang benar adalah D.

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