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Nilai x yang memenuhi 2−3xlog(x2−2x+2)=2log 4 adalah ...

Pertanyaan

Nilai begin mathsize 14px style x end style yang memenuhi begin mathsize 14px style scriptbase log open parentheses x squared minus 2 x plus 2 close parentheses end scriptbase presuperscript 2 minus 3 x end presuperscript equals scriptbase log space 4 end scriptbase presuperscript 2 end style adalah ...

  1. begin mathsize 14px style 1 third end style 

  2. begin mathsize 14px style 1 end style 

  3. begin mathsize 14px style 2 over 3 end style 

  4. begin mathsize 14px style 4 end style 

  5. begin mathsize 14px style 1 fourth end style 

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Diketahui:

Persamaan logaritma begin mathsize 14px style scriptbase log open parentheses x squared minus 2 x plus 2 close parentheses end scriptbase presuperscript 2 minus 3 x end presuperscript equals scriptbase log space 4 end scriptbase presuperscript 2 end style.

Ingat sifat logaritma:

begin mathsize 14px style scriptbase log space a to the power of n equals n end scriptbase presuperscript a end style

Persamaan logaritma menjadi:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log open parentheses x squared minus 2 x plus 2 close parentheses end scriptbase presuperscript 2 minus 3 x end presuperscript end cell equals cell scriptbase log space 4 end scriptbase presuperscript 2 end cell row cell scriptbase log open parentheses x squared minus 2 x plus 2 close parentheses end scriptbase presuperscript 2 minus 3 x end presuperscript end cell equals cell scriptbase log space 2 squared end scriptbase presuperscript 2 end cell row cell scriptbase log open parentheses x squared minus 2 x plus 2 close parentheses end scriptbase presuperscript 2 minus 3 x end presuperscript end cell equals 2 row cell open parentheses 2 minus 3 x close parentheses squared end cell equals cell x squared minus 2 x plus 2 end cell row cell 9 x squared minus 12 x plus 4 end cell equals cell x squared minus 2 x plus 2 end cell row cell 9 x squared minus x squared minus 12 x plus 2 x plus 4 minus 2 end cell equals 0 row cell 8 x squared minus 10 x plus 2 end cell equals 0 row cell 4 x squared minus 5 x plus 1 end cell equals 0 row cell open parentheses 4 x minus 1 close parentheses open parentheses x minus 1 close parentheses end cell equals 0 end table end style

Dengan,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x minus 1 end cell equals 0 row cell 4 x end cell equals 1 row x equals cell 1 fourth end cell row blank blank blank row cell x minus 1 end cell equals 0 row x equals 1 end table end style

Basis persamaan logaritma begin mathsize 14px style scriptbase log open parentheses x squared minus 2 x plus 2 close parentheses end scriptbase presuperscript 2 minus 3 x end presuperscript equals scriptbase log space 4 end scriptbase presuperscript 2 end style merupakan bentuk fungsi, tentukan terlebih dahulu syarat basisnya, yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 minus 3 x end cell greater than 0 row cell negative 3 x end cell greater than cell negative 2 end cell row x less than cell 2 over 3 end cell end table end style dan begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 minus 3 x end cell not equal to 1 row cell negative 3 x end cell not equal to cell 1 minus 2 end cell row cell negative 3 x end cell not equal to cell negative 1 end cell row x not equal to cell 1 third end cell end table end style

Karena syarat basis persamaan logaritma begin mathsize 14px style x less than 2 over 3 end style dan begin mathsize 14px style x not equal to 1 third end style, maka nilai begin mathsize 14px style x end style yang memenuhi adalah begin mathsize 14px style 1 fourth end style.

Jadi, jawaban yang tepat adalah E.

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