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Pertanyaan

Jika size 14px log presubscript blank presuperscript size 14px w size 14px invisible function application size 14px z size 14px equals size 14px 5, log presubscript blank presuperscript y invisible function application z equals 2, dan log presubscript blank presuperscript x invisible function application y equals 4, maka nilai dari begin mathsize 14px style log presubscript blank presuperscript x y end presuperscript invisible function application w z end style adalah ....  

  1. size 14px 72 over size 14px 25 

  2. 48 over 25  

  3.  32 over 25  

  4. 16 over 25  

  5. 8 over 25  

S. Suharni

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Dengan menggunakan sifat-sifat pada logaritma didapat persamaan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript blank presuperscript x y end presuperscript invisible function application w z end cell equals cell log presubscript blank presuperscript x y end presuperscript invisible function application w plus log presubscript blank presuperscript x y end presuperscript invisible function application z end cell row cell log presubscript blank presuperscript x y end presuperscript invisible function application w z end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript w invisible function application x y end fraction plus fraction numerator 1 over denominator log presubscript blank presuperscript z invisible function application x y end fraction end cell row cell log presubscript blank presuperscript x y end presuperscript invisible function application w z end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript w invisible function application x plus log presubscript blank presuperscript w invisible function application y end fraction plus fraction numerator 1 over denominator log presubscript blank presuperscript z invisible function application x plus log presubscript blank presuperscript z invisible function application y end fraction end cell end table  


Pada soal diketahui log presubscript blank presuperscript y invisible function application z equals 2 sehingga didapat nilai log presubscript blank presuperscript z invisible function application y sebagai berikut.

log presubscript blank presuperscript z invisible function application y equals fraction numerator 1 over denominator log presubscript blank presuperscript y invisible function application z end fraction equals 1 half 

Kemudian, dengan menggunakan sifat logaritma didapat nilai log presubscript blank presuperscript x invisible function application z sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript blank presuperscript x invisible function application z end cell equals cell log presubscript blank presuperscript x invisible function application y times log presubscript blank presuperscript y invisible function application z end cell row blank equals cell 4 times 2 end cell row blank equals 8 end table 

Oleh karena itu, didapat nilai log presubscript blank presuperscript z invisible function application x sebagai berikut.

log presubscript blank presuperscript z invisible function application x equals fraction numerator 1 over denominator log presubscript blank presuperscript x invisible function application z end fraction equals 1 over 8  

Selanjutnya, nilai log presubscript blank presuperscript w invisible function application y dan log presubscript blank presuperscript w invisible function application x dapat dicari sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript blank presuperscript w invisible function application y end cell equals cell log presubscript blank presuperscript w invisible function application z times log presubscript blank presuperscript z invisible function application y end cell row blank equals cell 5 times 1 half end cell row blank equals cell 5 over 2 end cell end table  

dan

table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript blank presuperscript w invisible function application x end cell equals cell log presubscript blank presuperscript w invisible function application z times log presubscript blank presuperscript z invisible function application x end cell row blank equals cell 5 times 1 over 8 end cell row blank equals cell 5 over 8 end cell end table  

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row cell log presubscript blank presuperscript x y end presuperscript invisible function application w z end cell equals cell fraction numerator 1 over denominator log presubscript blank presuperscript w invisible function application x plus log presubscript blank presuperscript w invisible function application y end fraction plus fraction numerator 1 over denominator log presubscript blank presuperscript z invisible function application x plus log presubscript blank presuperscript z invisible function application y end fraction end cell row blank equals cell fraction numerator 1 over denominator 5 over 8 plus 5 over 2 end fraction plus fraction numerator 1 over denominator 1 over 8 plus 1 half end fraction end cell row blank equals cell fraction numerator 1 over denominator 5 over 8 plus 20 over 8 end fraction plus fraction numerator 1 over denominator 1 over 8 plus 4 over 8 end fraction end cell row blank equals cell fraction numerator 1 over denominator 25 over 8 end fraction plus fraction numerator 1 over denominator 5 over 8 end fraction end cell row blank equals cell 8 over 25 plus 8 over 5 end cell row blank equals cell 8 over 25 plus 40 over 25 end cell row blank equals cell 48 over 25 end cell end table  

Jadi, jawaban yang tepat adalah B.

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