Jika 31log (3x+2)≥−2, maka nilai x yang memenuhi adalah ....

Pertanyaan

Jika ${}^\frac13\log\;\left(3x+2\right)\geq-2$ , maka nilai $x$ yang memenuhi adalah ....

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat kembali:

n times log presuperscript a space b equals log presuperscript a space b to the power of n log presuperscript a space f open parentheses x close parentheses greater or equal than log presuperscript a space p comma space 0 less than a less than 1 rightwards arrow f open parentheses x close parentheses less or equal than p semicolon space f open parentheses x close parentheses greater than 0

Diketahui pertidaksamaan log presuperscript 1 third end presuperscript space open parentheses 3 x plus 2 close parentheses greater or equal than negative 2 , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 1 third end presuperscript space open parentheses 3 x plus 2 close parentheses end cell greater or equal than cell negative 2 end cell row cell log presuperscript 1 third end presuperscript space open parentheses 3 x plus 2 close parentheses end cell greater or equal than cell negative 2 times log presuperscript 1 third end presuperscript space open parentheses 1 third close parentheses end cell row cell log presuperscript 1 third end presuperscript space open parentheses 3 x plus 2 close parentheses end cell greater or equal than cell log presuperscript 1 third end presuperscript space open parentheses 1 third close parentheses to the power of negative 2 end exponent end cell row cell log presuperscript 1 third end presuperscript space open parentheses 3 x plus 2 close parentheses end cell greater or equal than cell log presuperscript 1 third end presuperscript space open parentheses 1 over open parentheses begin display style 1 third end style close parentheses squared close parentheses end cell row cell log presuperscript 1 third end presuperscript space open parentheses 3 x plus 2 close parentheses end cell greater or equal than cell log presuperscript 1 third end presuperscript space open parentheses fraction numerator 1 over denominator begin display style 1 over 9 end style end fraction close parentheses end cell row cell log presuperscript 1 third end presuperscript space open parentheses 3 x plus 2 close parentheses end cell greater or equal than cell log presuperscript 1 third end presuperscript space 9 end cell end table$

Sehingga:

Untuk

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell less or equal than p row cell 3 x plus 2 end cell less or equal than 9 row cell 3 x end cell less or equal than cell 9 minus 2 end cell row cell 3 x end cell less or equal than 7 row x less or equal than cell 7 over 3 end cell end table

Untuk

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell greater than 0 row cell 3 x plus 2 end cell greater than 0 row cell 3 x end cell greater than cell negative 2 end cell row x greater than cell negative 2 over 3 end cell end table

nilai yang memenuhi adalah negative 2 over 3 less than x less or equal than 7 over 3 .

Jadi, jawaban yang benar adalah D.