Himpunan penyelesaian pertidaksamaan 2×9log2 x−7×9log x>−3 adalah...

Pertanyaan

Himpunan penyelesaian pertidaksamaan 2 cross times log presuperscript 9 superscript 2 space x minus 7 cross times log presuperscript 9 space x greater than negative 3 adalah...

  1. open curly brackets x vertical line 1 half less than x less than 3 close curly brackets 

  2. open curly brackets x vertical line x less than 1 half logical or x greater than 3 close curly brackets 

  3. open curly brackets x vertical line x less than 3 logical or x greater than 729 close curly brackets 

  4. open curly brackets x vertical line 0 less than x less than 3 logical or x greater than 729 close curly brackets 

  5. open curly brackets x vertical line 5 less than x less than 9 logical or x greater than 729 close curly brackets 

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

2 cross times log presuperscript 9 superscript 2 space x minus 7 cross times log presuperscript 9 space x greater than negative 3 

Misal log presuperscript 9 space x equals n maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 open square brackets log presuperscript 9 superscript 2 space x close square brackets minus 7 open square brackets log presuperscript 9 space x close square brackets end cell greater than cell negative 3 end cell row cell 2 open square brackets open parentheses log presuperscript 9 space x close parentheses squared close square brackets minus 7 open square brackets log presuperscript 9 space x close square brackets end cell greater than cell negative 3 end cell row cell 2 open parentheses n squared close parentheses minus 7 open parentheses n close parentheses end cell greater than cell negative 3 end cell row cell 2 n squared minus 7 n plus 3 end cell greater than 0 row cell open parentheses 2 n minus 1 close parentheses open parentheses n minus 3 close parentheses end cell greater than 0 row cell 2 n minus 1 end cell greater than 0 row cell 2 n end cell greater than 1 row n greater than cell 1 half end cell row cell n minus 3 end cell greater than 0 row n greater than 3 row blank blank blank end table 

Menentukan nilai x

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 9 space x end cell less than n row cell log presuperscript 9 space x end cell less than cell 1 half end cell row x less than cell 9 to the power of 1 half end exponent end cell row x less than cell square root of 9 end cell row x less than 3 row cell log presuperscript 9 space x end cell greater than n row cell log presuperscript 9 space x end cell greater than 3 row x greater than cell 9 cubed end cell row x greater than 729 end table 

Jadi, himpunan penyelesaiannya adalah  open curly brackets x vertical line x less than 3 logical or x greater than 729 close curly brackets.

Oleh karena itu, jawaban yang benar adalah C.

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