Roboguru

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.

107

0.0 (0 rating)

Pertanyaan serupa

Nilai x yang memenuhi persamaan adalah ....

77

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia