Nilai x yang memenuhi persamaan 4−102x+1​=2⋅22⋅23⋅⋯⋅2xadalah ....

Pertanyaan

Nilai x yang memenuhi persamaan 2 to the power of x plus 1 end exponent over 4 to the power of negative 10 end exponent equals 2 times 2 squared times 2 cubed times horizontal ellipsis times 2 to the power of xadalah .... 

  1. 3   

  2. 4 

  3. 5  

  4. 6 

  5.  7 

A. Allamah

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.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
  • 1 over a to the power of negative m end exponent equals a to the power of m
  • a to the power of m a to the power of n equals a to the power of m plus n end exponent
  • 1 plus 2 plus 3 plus midline horizontal ellipsis plus n equals fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction dengan n greater than 0

Oleh karena bentuk persamaan dapat diubah menjadi seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of x plus 1 end exponent over 4 to the power of negative 10 end exponent end cell equals cell 2 times 2 squared times 2 cubed times horizontal ellipsis times 2 to the power of x end cell row cell 2 to the power of x plus 1 end exponent over open parentheses 2 squared close parentheses to the power of negative 10 end exponent end cell equals cell 2 to the power of 1 times 2 squared times 2 cubed times horizontal ellipsis times 2 to the power of x end cell row cell 2 to the power of x plus 1 end exponent over 2 to the power of negative 20 end exponent end cell equals cell 2 to the power of 1 plus 2 plus 3 plus horizontal ellipsis plus x end exponent end cell row cell 2 to the power of x plus 1 end exponent times 2 to the power of 20 end cell equals cell 2 to the power of fraction numerator x open parentheses x plus 1 close parentheses over denominator 2 end fraction end exponent end cell row cell 2 to the power of x plus 1 plus 20 end exponent end cell equals cell 2 to the power of fraction numerator x squared plus x over denominator 2 end fraction end exponent end cell row cell 2 to the power of x plus 21 end exponent end cell equals cell 2 to the power of fraction numerator x squared plus x over denominator 2 end fraction end exponent end cell end table

sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x squared plus x over denominator 2 end fraction end cell equals cell x plus 21 end cell row cell x squared plus x end cell equals cell 2 open parentheses x plus 21 close parentheses end cell row cell x squared plus x end cell equals cell 2 x plus 42 end cell row cell x squared plus x minus 2 x end cell equals 42 row cell x squared plus x minus 2 x minus 42 end cell equals 0 row cell x squared minus x plus negative 42 end cell equals 0 row cell open parentheses x minus 7 close parentheses open parentheses x plus 6 close parentheses end cell equals 0 row x equals cell 7 space space space logical or space space space x equals negative 6 end cell end table  

Oleh karena x greater than 0, maka nilai x yang memenuhi persamaan 2 to the power of x plus 1 end exponent over 4 to the power of negative 10 end exponent equals 2 times 2 squared times 2 cubed times horizontal ellipsis times 2 to the power of x adalah 7.

Oleh karena itu, jawaban yang benar adalah E.space 

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