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Nilai x yang memenuhi persamaan 223x−1​=481−3x​adalah ....

Pertanyaan

Nilai x yang memenuhi persamaan 2 square root of 2 to the power of 3 x minus 1 end exponent end root equals 4 square root of 8 to the power of 1 minus 3 x end exponent end rootadalah ....

  1. 1 

  2. 1 half 

  3. 1 third 

  4. 1 fourth 

  5. 1 fifth 

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.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 dan a not equal to 0 maka f open parentheses x close parentheses equals g open parentheses x close parentheses
  • a equals a to the power of 1
  • 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 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

Oleh karena persamaan dapat diubah menjadi bentuk seperti berikut:

2 square root of 2 to the power of 3 x minus 1 end exponent end root equals 4 square root of 8 to the power of 1 minus 3 x end exponent end root 2 to the power of 1 square root of 2 to the power of 3 x minus 1 end exponent end root equals 2 squared square root of open parentheses 2 cubed close parentheses to the power of 1 minus 3 x end exponent end root 2 to the power of 1 square root of 2 to the power of 3 x minus 1 end exponent end root equals 2 squared square root of 2 to the power of 3 minus 9 x end exponent end root 2 to the power of 1 times 2 to the power of fraction numerator 3 x minus 1 over denominator 2 end fraction end exponent equals 2 squared times 2 to the power of fraction numerator 3 minus 9 x over denominator 2 end fraction end exponent 2 to the power of 1 plus fraction numerator 3 x minus 1 over denominator 2 end fraction end exponent equals 2 to the power of 2 plus fraction numerator 3 minus 9 x over denominator 2 end fraction end exponent 2 to the power of 2 over 2 plus fraction numerator 3 x minus 1 over denominator 2 end fraction end exponent equals 2 to the power of 4 over 2 plus fraction numerator 3 minus 9 x over denominator 2 end fraction end exponent 2 to the power of fraction numerator 3 x minus 1 plus 2 over denominator 2 end fraction end exponent equals 2 to the power of fraction numerator 4 plus 3 minus 9 x over denominator 2 end fraction end exponent 2 to the power of fraction numerator 3 x plus 1 over denominator 2 end fraction end exponent equals 2 to the power of fraction numerator 7 minus 9 x over denominator 2 end fraction end exponent 

maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 x plus 1 over denominator 2 end fraction end cell equals cell fraction numerator 7 minus 9 x over denominator 2 end fraction end cell row cell 3 x plus 1 end cell equals cell 7 minus 9 x end cell row cell 3 x end cell equals cell 7 minus 9 x minus 1 end cell row cell 3 x plus 9 x end cell equals cell 7 minus 1 end cell row cell 12 x end cell equals 6 row x equals cell 6 over 12 end cell row x equals cell fraction numerator 6 divided by 6 over denominator 12 divided by 6 end fraction end cell row x equals cell 1 half end cell end table 

Oleh karena itu, jawaban yang benar adalah B.space 

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