Roboguru

Pertanyaan

Nilai x agar persamaan fraction numerator 1 plus log presuperscript 2 space open parentheses x squared plus 3 close parentheses over denominator log presuperscript 2 space x plus log presuperscript 2 space open parentheses 17 minus 3 x close parentheses end fraction equals 1 bernilai benar adalah ....

  1. tidak ada 

  2. x equals negative 2 over 5 

  3. x equals negative 3 

  4. x equals 1 third

  5. x equals 2 over 5 space atau space x equals 3 

E. Dwi

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Perlu diingat bahwa:

log presuperscript a space a equals 1 log presuperscript a space left parenthesis b c right parenthesis equals log presuperscript a space b plus log presuperscript a space c log presuperscript a space f left parenthesis x right parenthesis equals log presuperscript a space g left parenthesis x right parenthesis left right double arrow f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis

Perhatikan perhitungan berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 plus log presuperscript 2 space open parentheses x squared plus 3 close parentheses over denominator log presuperscript 2 space x plus log presuperscript 2 space open parentheses 17 minus 3 x close parentheses end fraction end cell equals 1 row cell 1 plus log presuperscript 2 space open parentheses x squared plus 3 close parentheses end cell equals cell log presuperscript 2 space x plus log presuperscript 2 space open parentheses 17 minus 3 x close parentheses end cell row cell log presuperscript 2 space 2 plus log presuperscript 2 space open parentheses x squared plus 3 close parentheses end cell equals cell log presuperscript 2 space x plus log presuperscript 2 space open parentheses 17 minus 3 x close parentheses end cell row cell log presuperscript 2 space open parentheses 2 open parentheses x squared plus 3 close parentheses close parentheses end cell equals cell log presuperscript 2 space open parentheses x open parentheses 17 minus 3 x close parentheses close parentheses end cell row cell log presuperscript 2 space open parentheses 2 x squared plus 6 close parentheses end cell equals cell log presuperscript 2 space open parentheses 17 x minus 3 x squared close parentheses end cell row cell 2 x squared plus 6 end cell equals cell 17 x minus 3 x squared end cell row cell 5 x squared minus 17 x plus 6 end cell equals 0 row cell open parentheses 5 x minus 2 close parentheses open parentheses x minus 3 close parentheses end cell equals 0 end table

5 x minus 2 equals 0 space atau space x minus 3 equals 0 5 x equals 2 space atau space x equals 3 x equals 2 over 5 space atau space x equals 3

Sehingga, nilai x agar persamaan fraction numerator 1 plus log presuperscript 2 space open parentheses x squared plus 3 close parentheses over denominator log presuperscript 2 space x plus log presuperscript 2 space open parentheses 17 minus 3 x close parentheses end fraction equals 1 bernilai benar adalah x equals 2 over 5 atau x equals 3.

Jadi, jawaban yang tepat adalah E.

12

0.0 (0 rating)

Pertanyaan serupa

Jika 3log3log(x+1)−3log3log3log9=1 maka x=...

15

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