NIlai-nilai x yang memenuhi pertidaksamaan 2x−2​<38x2−4​ adalah ....

Pertanyaan

NIlai-nilai x yang memenuhi pertidaksamaan square root of 2 to the power of x minus 2 end exponent end root less than cube root of 8 to the power of x squared minus 4 end exponent end root adalah ....

  1. negative 2 less than x less than 1 1 half

  2. negative 1 1 half less than x less than 2 

  3. x less than negative 2 space atau space x greater than 1 1 half 

  4. x less than negative 1 1 half space atau space x greater than 2  

  5. x less than negative 2 space atau space x greater than 2 

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah D.

Jika a to the power of f open parentheses x close parentheses end exponent less than a to the power of g open parentheses x close parentheses end exponent untuk a greater than 1, maka f open parentheses x close parentheses less than g open parentheses x close parentheses.

Ingat sifat-sifat eksponen berikut.

a to the power of m over n end exponent equals n-th root of a to the power of m end root

open parentheses a to the power of m close parentheses to the power of n equals a to the power of m times n end exponent

Penyelesaian dari pertidaksamaan square root of 2 to the power of x minus 2 end exponent end root less than cube root of 8 to the power of x squared minus 4 end exponent end root adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 2 to the power of x minus 2 end exponent end root end cell less than cell cube root of 8 to the power of x squared minus 4 end exponent end root end cell row cell 2 to the power of fraction numerator x minus 2 over denominator 2 end fraction end exponent end cell less than cell 8 to the power of fraction numerator x squared minus 4 over denominator 3 end fraction end exponent end cell row cell 2 to the power of fraction numerator x minus 2 over denominator 2 end fraction end exponent end cell less than cell open parentheses 2 cubed close parentheses to the power of fraction numerator x squared minus 4 over denominator 3 end fraction end exponent end cell row cell 2 to the power of fraction numerator x minus 2 over denominator 2 end fraction end exponent end cell less than cell 2 to the power of x squared minus 4 end exponent end cell row cell fraction numerator x minus 2 over denominator 2 end fraction end cell less than cell x squared minus 4 end cell row cell x minus 2 end cell less than cell 2 x squared minus 8 end cell row cell 2 x squared minus x minus 6 end cell greater than 0 row cell open parentheses 2 x plus 3 close parentheses open parentheses x minus 2 close parentheses end cell greater than 0 end table

Pembuat nol: x equals negative 3 over 2 equals negative 1 1 half atau x equals 2 

Penyelesaian pertidaksamaan tersebut adalah x less than negative 1 1 half space atau space x greater than 2

Oleh karena itu, jawaban yang benar adalah D.

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