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Pertanyaan

Jika begin mathsize 14px style x subscript 1 end style dan begin mathsize 14px style x subscript 2 end style memenuhi persamaan begin mathsize 14px style 2 open parentheses scriptbase log space x end scriptbase presuperscript 4 close parentheses squared minus 6 open parentheses scriptbase log space x over 2 end scriptbase presuperscript 4 close parentheses plus 1 equals 0 end style. Maka begin mathsize 14px style x subscript 1 plus x subscript 2 equals end style ...

  1. begin mathsize 14px style 3 end style 

  2. begin mathsize 14px style 4 end style 

  3. begin mathsize 14px style 6 end style 

  4. begin mathsize 14px style 12 end style 

  5. begin mathsize 14px style 20 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 2 open parentheses scriptbase log space x end scriptbase presuperscript 4 close parentheses squared minus 6 open parentheses scriptbase log space x over 2 end scriptbase presuperscript 4 close parentheses plus 1 equals 0 end style.

Jika begin mathsize 14px style scriptbase log space x equals a end scriptbase presuperscript 4 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 left parenthesis scriptbase log space x end scriptbase presuperscript 4 right parenthesis squared minus 6 open parentheses scriptbase log space x over 2 end scriptbase presuperscript 4 close parentheses plus 1 end cell equals 0 row cell 2 left parenthesis scriptbase log space x end scriptbase presuperscript 4 right parenthesis squared minus 6 open parentheses scriptbase log space x minus scriptbase log space 2 end scriptbase presuperscript 4 end scriptbase presuperscript 4 close parentheses plus 1 end cell equals 0 row cell 2 left parenthesis scriptbase log space x end scriptbase presuperscript 4 right parenthesis squared minus 6 open parentheses scriptbase log space x minus scriptbase log space 2 end scriptbase presuperscript 2 squared end presuperscript end scriptbase presuperscript 4 close parentheses plus 1 end cell equals 0 row cell 2 left parenthesis scriptbase log space x end scriptbase presuperscript 4 right parenthesis squared minus 6 open parentheses scriptbase log space x minus 1 half end scriptbase presuperscript 4 close parentheses plus 1 end cell equals 0 row cell 2 a squared minus 6 open parentheses a minus 1 half close parentheses plus 1 end cell equals 0 row cell 2 a squared minus 6 a plus 3 plus 1 end cell equals 0 row cell 2 a squared minus 6 a plus 4 end cell equals 0 row cell 2 open parentheses a squared minus 3 a plus 2 close parentheses end cell equals 0 row cell 2 open parentheses a open parentheses a minus 1 close parentheses minus 2 open parentheses a minus 1 close parentheses close parentheses end cell equals 0 row cell 2 open parentheses a minus 1 close parentheses open parentheses a minus 2 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 a minus 1 end cell equals 0 row a equals 1 row blank blank blank row cell a minus 2 end cell equals 0 row a equals 2 end table end style

Dimisalkan begin mathsize 14px style scriptbase log space x equals a end scriptbase presuperscript 4 end style, maka persamaan logaritma menjadi:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log space x subscript 1 end scriptbase presuperscript 4 end cell equals a row cell scriptbase log space x subscript 1 end scriptbase presuperscript 4 end cell equals 1 row cell x subscript 1 end cell equals cell 4 to the power of 1 end cell row cell x subscript 1 end cell equals 4 row blank blank blank row cell scriptbase log space x subscript 2 end scriptbase presuperscript 4 end cell equals a row cell scriptbase log space x subscript 2 end scriptbase presuperscript 4 end cell equals 2 row cell x subscript 2 end cell equals cell 4 squared end cell row cell x subscript 2 end cell equals 16 end table end style

Maka begin mathsize 14px style x subscript 1 plus x subscript 2 equals end stylebegin mathsize 14px style 4 plus 16 equals 20 end style.

Jadi, jawaban yang tepat adalah E.

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