Pertanyaan

Carilah semua nilai x yang memenuhi pertidaksamaan berikut. b. 4 lo g ( 3 x + 4 ) > 2 lo g ( x + 4 ) + 2 1 lo g 2

Carilah semua nilai $x$ yang memenuhi pertidaksamaan berikut.

b. $^{4} lo g (3 x + 4) >^{2} lo g (x + 4) +^{\frac{1}{2}} lo g 2$

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai yang memenuhi adalah .

nilai

yang memenuhi adalah 0 less than x less than 4

Pembahasan

Ingat sifat-sifat bentuk logaritma: Pada pertidaksamaan logaritma untuk jika: Diketahui maka: sehingga nilai yang memenuhi . syarat numerus 1): syarat numerus 2): Berdasarkan syarat numerus dan maka irisanya adalah . Dengan demikiannilai yang memenuhi adalah .

Ingat sifat-sifat bentuk logaritma:

Pada pertidaksamaan logaritma untuk a greater than 1 jika:

log presuperscript a space f open parentheses x close parentheses greater than log presuperscript a space g open parentheses x close parentheses rightwards arrow f open parentheses x close parentheses greater than g open parentheses x close parentheses comma space f open parentheses x close parentheses greater than 0 comma space dan space g open parentheses x close parentheses greater than 0

Diketahui log presuperscript 4 space open parentheses 3 x plus 4 close parentheses greater than log presuperscript 2 space open parentheses x plus 4 close parentheses plus log presuperscript begin inline style 1 half end style end presuperscript space 2 maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 4 space open parentheses 3 x plus 4 close parentheses end cell greater than cell log presuperscript 2 space open parentheses x plus 4 close parentheses plus log presuperscript begin inline style 1 half end style end presuperscript space 2 end cell row cell log presuperscript 2 squared end presuperscript space open parentheses 3 x plus 4 close parentheses end cell greater than cell log presuperscript 2 space open parentheses x plus 4 close parentheses plus log presuperscript begin inline style 2 to the power of negative 1 end exponent end style end presuperscript space 2 end cell row cell 1 half times log presuperscript 2 space open parentheses 3 x plus 4 close parentheses end cell greater than cell log presuperscript 2 space open parentheses x plus 4 close parentheses plus open parentheses negative 1 close parentheses log presuperscript begin inline style 2 end style end presuperscript space 2 end cell row cell log presuperscript 2 space open parentheses 3 x plus 4 close parentheses to the power of begin inline style 1 half end style end exponent end cell greater than cell log presuperscript 2 space open parentheses x plus 4 close parentheses minus log presuperscript 2 space 2 end cell row cell log presuperscript 2 space open parentheses 3 x plus 4 close parentheses to the power of begin inline style 1 half end style end exponent end cell greater than cell log presuperscript 2 space fraction numerator open parentheses x plus 4 close parentheses over denominator 2 end fraction end cell row cell space open parentheses 3 x plus 4 close parentheses to the power of begin inline style 1 half end style end exponent end cell greater than cell fraction numerator open parentheses x plus 4 close parentheses over denominator 2 end fraction end cell row cell open parentheses open parentheses 3 x plus 4 close parentheses to the power of begin inline style 1 half end style end exponent close parentheses squared end cell greater than cell open parentheses fraction numerator open parentheses x plus 4 close parentheses over denominator 2 end fraction close parentheses squared end cell row cell 3 x plus 4 end cell greater than cell open parentheses x plus 4 close parentheses squared over 4 end cell row cell open parentheses x plus 4 close parentheses squared over 4 minus 3 x plus 4 end cell less than 0 row cell open parentheses x plus 4 close parentheses squared over 4 minus fraction numerator 4 open parentheses 3 x plus 4 close parentheses over denominator 4 end fraction end cell less than 0 row cell fraction numerator x squared plus 8 x plus 16 over denominator 4 end fraction minus fraction numerator 12 x plus 16 over denominator 4 end fraction end cell less than 0 row cell fraction numerator x squared minus 4 x over denominator 4 end fraction end cell less than 0 row cell fraction numerator x open parentheses x minus 4 close parentheses over denominator 4 end fraction end cell less than 0 end table$

sehingga nilai yang memenuhi 0 less than x less than 4 .

syarat numerus 1):

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 4 end cell greater than 0 row x greater than cell negative 4 over 3 end cell end table

syarat numerus 2):

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 4 end cell greater than 0 row x greater than cell negative 4 end cell end table

Berdasarkan syarat numerus dan 0 less than x less than 4 maka irisanya adalah .

Dengan demikian nilai yang memenuhi adalah 0 less than x less than 4 .