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Penyelesaian dari persamaan 2553x​⋅1253x​=52x125x−2​ adalah ....

Pertanyaan

Penyelesaian dari persamaan 25 square root of 5 to the power of 3 x end exponent end root times square root of 125 to the power of 3 x end exponent end root equals 125 to the power of x minus 2 end exponent over 5 to the power of 2 x end exponent adalah .... 

  1. negative 1 comma 8  

  2. negative 1 comma 6  

  3. negative 1 comma 4 

  4. negative 0 comma 8 

  5. 1 comma 6 

I. Ridha

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

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 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
  • 1 over a to the power of m equals a to the power of negative m end exponent dengan a not equal to 0
  • 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

Dengan demikian, 

table attributes columnalign right center left columnspacing 0px end attributes row cell 25 square root of 5 to the power of 3 x end exponent end root times square root of 125 to the power of 3 x end exponent end root end cell equals cell 125 to the power of x minus 2 end exponent over 5 to the power of 2 x end exponent end cell row cell 5 squared times square root of 5 to the power of 3 x end exponent end root times square root of open parentheses 5 cubed close parentheses to the power of 3 x end exponent end root end cell equals cell open parentheses 5 cubed close parentheses to the power of x minus 2 end exponent times 5 to the power of negative 2 x end exponent end cell row cell 5 squared times square root of 5 to the power of 3 x end exponent end root times square root of 5 to the power of 9 x end exponent end root end cell equals cell 5 to the power of 3 x minus 6 end exponent times 5 to the power of negative 2 x end exponent end cell row cell 5 squared times 5 to the power of fraction numerator 3 x over denominator 2 end fraction end exponent times 5 to the power of fraction numerator 9 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of 3 x minus 6 end exponent times 5 to the power of negative 2 x end exponent end cell row cell 5 to the power of 2 plus fraction numerator 3 x over denominator 2 end fraction plus fraction numerator 9 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of 3 x minus 6 plus open parentheses negative 2 x close parentheses end exponent end cell row cell 5 to the power of 4 over 2 plus fraction numerator 3 x over denominator 2 end fraction plus fraction numerator 9 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of 3 x minus 6 plus open parentheses negative 2 x close parentheses end exponent end cell row cell 5 to the power of fraction numerator 4 plus 3 x plus 9 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of 3 x minus 6 plus open parentheses negative 2 x close parentheses end exponent end cell row cell 5 to the power of fraction numerator 4 plus 12 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of x minus 6 end exponent end cell end table

sehingga karena a equals 5 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 fraction numerator 4 plus 12 x over denominator 2 end fraction end cell equals cell x minus 6 end cell row cell 4 plus 12 x end cell equals cell open parentheses x minus 6 close parentheses cross times 2 end cell row cell 4 plus 12 x end cell equals cell 2 x minus 12 end cell row cell 12 x end cell equals cell 2 x minus 12 minus 4 end cell row cell 12 x minus 2 x end cell equals cell negative 12 minus 4 end cell row cell 10 x end cell equals cell negative 16 end cell row x equals cell fraction numerator negative 16 over denominator 10 end fraction end cell row x equals cell negative 1 comma 6 end cell end table

Oleh karena itu, jawaban yang benar adalah B.space 

120

5.0 (3 rating)

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