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Jika  3927​​​=3yx​, maka nilai x+y adalah ....

Pertanyaan

Jika  square root of 3 square root of 9 square root of 27 end root end root equals 3 to the power of x over y end exponent, maka nilai x plus y adalah .... 
 

  1. 11

  2. 15

  3. 18

  4. 19

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Pada bentuk akar, berlaku aturan

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of a end cell equals cell a to the power of 1 half end exponent end cell row cell square root of a to the power of m end root end cell equals cell a to the power of m over 2 end exponent end cell row cell n-th root of a to the power of m end root end cell equals cell a to the power of m over n end exponent end cell row cell open parentheses a to the power of m close parentheses to the power of n end cell equals cell a to the power of m n end exponent end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 3 square root of 9 square root of 27 end root end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 1 square root of 3 squared square root of 3 cubed end root end root end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 1 square root of 3 squared open parentheses 3 to the power of 3 over 2 end exponent close parentheses end root end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 1 square root of 3 to the power of 2 plus 3 over 2 end exponent end root end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 1 square root of 3 to the power of 4 over 2 plus 3 over 2 end exponent end root end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 1 square root of 3 to the power of 7 over 2 end exponent end root end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 1 open parentheses 3 to the power of 7 over 2 divided by 2 end exponent close parentheses end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 1 open parentheses 3 to the power of 7 over 2 cross times 1 half end exponent close parentheses end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 1 open parentheses 3 to the power of 7 over 4 end exponent close parentheses end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 1 plus 7 over 4 end exponent end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 4 over 4 plus 7 over 4 end exponent end root end cell equals cell 3 to the power of x over y end exponent end cell row cell square root of 3 to the power of 11 over 4 end exponent end root end cell equals cell 3 to the power of x over y end exponent end cell row cell open parentheses 3 to the power of 11 over 4 end exponent close parentheses to the power of 1 half end exponent end cell equals cell 3 to the power of x over y end exponent end cell row cell open parentheses 3 to the power of 11 over 4 cross times 1 half end exponent close parentheses end cell equals cell 3 to the power of x over y end exponent end cell row cell 3 to the power of 11 over 8 end exponent end cell equals cell 3 to the power of x over y end exponent end cell row cell x over y end cell equals cell 11 over 8 end cell end table

Di dapatkan x equals 11 dan y equals 8. Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell straight x plus straight y end cell equals cell 11 plus 8 end cell row blank equals 19 end table

Jadi,  nilai x plus y adalah 19.


Oleh karena itu, jawaban yang benar adalah D.

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