Nilai x yang memenuhi pertidaksamaan log (x−2)+log (x+1)<2log (x+4) adalah...

Pertanyaan

Nilai $x$ yang memenuhi pertidaksamaan $\log\;\left(x-2\right)+\log\;\left(x+1\right)<2\log\;\left(x+4\right)$ adalah...

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

log space open parentheses x minus 2 close parentheses plus log space open parentheses x plus 1 close parentheses less than 2 log space open parentheses x plus 4 close parentheses

Ingat sifat logaritma!

log presuperscript a space b plus log presuperscript a space c equals log presuperscript a space b c

$table attributes columnalign right center left columnspacing 0px end attributes row cell log space open parentheses x minus 2 close parentheses plus log space open parentheses x plus 1 close parentheses end cell less than cell 2 log space open parentheses x plus 4 close parentheses end cell row cell log space open parentheses x minus 2 close parentheses open parentheses x plus 1 close parentheses end cell less than cell log space open parentheses x plus 4 close parentheses squared end cell row cell open parentheses x minus 2 close parentheses open parentheses x plus 1 close parentheses end cell less than cell open parentheses x plus 4 close parentheses squared end cell row cell x squared plus x minus 2 x minus 2 end cell less than cell x squared plus 4 x plus 4 x plus 16 end cell row cell x squared minus x minus 2 end cell less than cell x squared plus 8 x plus 16 end cell row cell negative x minus 8 x end cell less than cell 16 plus 2 end cell row cell negative 9 x end cell less than 18 row x greater than cell fraction numerator 18 over denominator negative 9 end fraction end cell row x greater than cell negative 2 end cell end table$

Jadi, nilai x yang memenuhi pertidaksamaan tersebut adalah x greater than negative 2 .

Oleh karena itu, jawaban yang benar adalah A.

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