Himpunan penyelesaian pertidaksamaan 4x+3<38x+5​ adalah ....

Pertanyaan

Himpunan penyelesaian pertidaksamaan 4 to the power of x plus 3 end exponent less than cube root of 8 to the power of x plus 5 end exponent end root adalah ....

  1. open curly brackets x vertical line x less than negative 1 close curly brackets  

  2. open curly brackets x vertical line x greater than negative 1 close curly brackets

  3. open curly brackets x vertical line x less than 1 comma 8 close curly brackets 

  4. open curly brackets x vertical line x greater than 1 comma 8 close curly brackets 

  5. open curly brackets x vertical line 0 less than x less than 1 close curly brackets 

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.space 

Pembahasan

Ingat kembali:

  • Jika a greater than 1 dan 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, maka f open parentheses x close parentheses less than g open parentheses x close parentheses 
  • open parentheses a to the power of m close parentheses to the power of n equals a to the power of m n end exponent 
  •  n-th root of a to the power of m end root equals a to the power of m over n end exponent 

Oleh karena pertidaksamaan dapat diubah menjadi bentuk seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 to the power of x plus 3 end exponent end cell less than cell cube root of 8 to the power of x plus 5 end exponent end root end cell row cell open parentheses 2 squared close parentheses to the power of x plus 3 end exponent end cell less than cell cube root of open parentheses 2 cubed close parentheses to the power of x plus 5 end exponent end root end cell row cell 2 to the power of 2 x plus 6 end exponent end cell less than cell cube root of 2 to the power of 3 open parentheses x plus 5 close parentheses end exponent end root end cell row cell 2 to the power of 2 x plus 6 end exponent end cell less than cell 2 to the power of fraction numerator 3 open parentheses x plus 5 close parentheses over denominator 3 end fraction end exponent end cell row cell 2 to the power of 2 x plus 6 end exponent end cell less than cell 2 to the power of x plus 5 end exponent end cell end table 

maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 6 end cell less than cell x plus 5 end cell row cell 2 x end cell less than cell x plus 5 minus 6 end cell row cell 2 x minus x end cell less than cell 5 minus 6 end cell row x less than cell negative 1 end cell end table

Jadi, himpunan penyelesaian pertidaksamaan 4 to the power of x plus 3 end exponent less than cube root of 8 to the power of x plus 5 end exponent end root adalah open curly brackets x vertical line x less than negative 1 close curly brackets.

Oleh karena itu, jawaban yang benar adalah A.space 

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