Supaya (251​)x−1=353x+1​ maka nilai x harus sama dengan ....

Pertanyaan

Supaya open parentheses 1 over 25 close parentheses to the power of x minus 1 end exponent equals cube root of 5 to the power of 3 x plus 1 end exponent end root maka nilai x harus sama dengan .... 

  1. 2 over 9 

  2. 4 over 9 

  3. 5 over 9 

  4. 2 over 5 

  5. 4 over 5 

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

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 dan a not equal to 0 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

Oleh karena bentuk persamaan dapat diubah menjadi seperti berikut:

open parentheses 1 over 25 close parentheses to the power of x minus 1 end exponent equals cube root of 5 to the power of 3 x plus 1 end exponent end root open parentheses 1 over 5 squared close parentheses to the power of x minus 1 end exponent equals 5 to the power of fraction numerator 3 x plus 1 over denominator 3 end fraction end exponent open parentheses 5 to the power of negative 2 end exponent close parentheses to the power of x minus 1 end exponent equals 5 to the power of fraction numerator 3 x plus 1 over denominator 3 end fraction end exponent 5 to the power of negative 2 x plus 2 end exponent equals 5 to the power of fraction numerator 3 x plus 1 over denominator 3 end fraction end exponent 5 to the power of negative 2 x plus 2 end exponent equals 5 to the power of fraction numerator 3 x plus 1 over denominator 3 end fraction end exponent

maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table row cell negative 2 x plus 2 equals fraction numerator 3 x plus 1 over denominator 3 end fraction end cell row cell open parentheses negative 2 x plus 2 close parentheses cross times 3 equals 3 x plus 1 end cell row cell negative 6 x plus 6 equals 3 x plus 1 end cell row cell negative 6 x equals 3 x plus 1 minus 6 end cell row cell negative 6 x minus 3 x equals 1 minus 6 end cell row cell negative 9 x equals negative 5 end cell row cell x equals fraction numerator negative 5 over denominator negative 9 end fraction end cell row cell x equals 5 over 9 end cell end table end cell end table 

Jadi, nilai x harus sama dengan 5 over 9.

Oleh karena itu, jawaban yang benar adalah C.space 

163

5.0 (3 rating)

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