Nilai x yang memenuhi persamaan 32x+1+32x+2=439x−2​ adalah ...

Pertanyaan

Nilai x yang memenuhi persamaan 3 to the power of 2 x plus 1 end exponent plus 3 to the power of 2 x plus 2 end exponent equals 4 cube root of 9 to the power of x minus 2 end exponent end root adalah ...

  1. negative 1 comma 25  

  2. negative 1 comma 5 

  3. negative 1 comma 75 

  4. negative 2 comma 25 

  5. negative 2 comma 75 

I. Ridha

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.space 

Pembahasan

Ingat kembali:

  • Jika a to the power of f open parentheses x close parentheses end exponent equals a to the power of g open parentheses x close parentheses end exponent dengan a greater than 0 dan a not equal to 1, maka f open parentheses x close parentheses equals g open parentheses x close parentheses
  • n-th root of a to the power of m end root equals a to the power of m over n end exponent dengan a greater than 0
  • a to the power of m a to the power of n equals a to the power of m plus n end exponent
  • 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

Oleh karena itu,  

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of 2 x plus 1 end exponent plus 3 to the power of 2 x plus 2 end exponent end cell equals cell 4 cube root of 9 to the power of x minus 2 end exponent end root end cell row cell open parentheses 3 times 3 to the power of 2 x end exponent close parentheses plus open parentheses 3 squared times 3 to the power of 2 x end exponent close parentheses end cell equals cell 4 cube root of open parentheses 3 squared close parentheses to the power of x minus 2 end exponent end root end cell row cell 12 times 3 to the power of 2 x end exponent end cell equals cell 4 cube root of 3 to the power of 2 x minus 4 end exponent end root end cell row cell 12 times 3 to the power of 2 x end exponent end cell equals cell 4 times 3 to the power of fraction numerator 2 x minus 4 over denominator 3 end fraction end exponent end cell row cell fraction numerator 12 times 3 to the power of 2 x end exponent over denominator 4 end fraction end cell equals cell 3 to the power of fraction numerator 2 x minus 4 over denominator 3 end fraction end exponent end cell row cell 3 times 3 to the power of 2 x end exponent end cell equals cell 3 to the power of fraction numerator 2 x minus 4 over denominator 3 end fraction end exponent end cell row cell 3 to the power of 2 x plus 1 end exponent end cell equals cell 3 to the power of fraction numerator 2 x minus 4 over denominator 3 end fraction end exponent end cell end table

sehingga karena a equals 3 yang berarti a greater than 0 dan a not equal to 1, maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 1 end cell equals cell fraction numerator 2 x minus 4 over denominator 3 end fraction end cell row cell 3 cross times open parentheses 2 x plus 1 close parentheses end cell equals cell 2 x minus 4 end cell row cell 6 x plus 3 end cell equals cell 2 x minus 4 end cell row cell 6 x end cell equals cell 2 x minus 4 minus 3 end cell row cell 6 x minus 2 x end cell equals cell negative 4 minus 3 end cell row cell 4 x end cell equals cell negative 7 end cell row x equals cell fraction numerator negative 7 over denominator 4 end fraction end cell row x equals cell negative 1 comma 75 end cell end table

Oleh karena itu, jawaban yang benar adalah C.space 

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