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Pertanyaan

Nilai p - q + r yang memenuhi persamaan 3 2 256 ​ ​ × 5 2 729 3 x 6 ​ ​ ​ = 2 p 3 q x r adalah ….

Nilai yang memenuhi persamaan  adalah ….

  1. begin mathsize 14px style 14 over 15 end style 

  2. begin mathsize 14px style 14 over 5 end style 

  3. begin mathsize 14px style 5 over 14 end style 

  4. begin mathsize 14px style 15 over 14 end style 

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H. Mahmud

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

jawaban yang tepat adalah A.

Pembahasan

Gunakan sifat akar: Maka Sehingga didapat . Dengan demikian, Jadi, jawaban yang tepat adalah A.

Gunakan sifat akar:

begin mathsize 14px style n-th root of x to the power of m end root equals x to the power of m over n end exponent end style  

Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of square root of 256 end root cross times fifth root of square root of 729 cube root of x to the power of 6 end root end root end root end cell equals cell 2 to the power of p 3 to the power of q x to the power of r end cell row cell cube root of square root of 16 squared end root end root cross times fifth root of square root of 3 to the power of 6 x squared end root blank end root end cell equals cell 2 to the power of p 3 to the power of q x to the power of r end cell row cell cube root of 16 cross times fifth root of 3 cubed times square root of x squared end root blank end root end cell equals cell 2 to the power of p 3 to the power of q x to the power of r end cell row cell cube root of 2 to the power of 4 end root cross times fifth root of 3 cubed x end root end cell equals cell 2 to the power of p 3 to the power of q x to the power of r end cell row cell 2 to the power of 4 over 3 end exponent blank 3 to the power of 3 over 5 end exponent blank x to the power of 1 fifth end exponent end cell equals cell 2 to the power of p 3 to the power of q x to the power of r end cell end table end style  

Sehingga didapat

begin mathsize 14px style p equals 4 over 3 comma blank q equals 3 over 5 blank dan blank r equals 1 fifth end style.

Dengan demikian,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p minus q plus r end cell equals cell 4 over 3 minus 3 over 5 plus 1 fifth end cell row blank equals cell 20 over 15 minus 9 over 15 plus 3 over 15 end cell row blank equals cell fraction numerator 20 minus 9 plus 3 over denominator 15 end fraction end cell row blank equals cell 14 over 15 end cell end table end style   

Jadi, jawaban yang tepat adalah A.

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