Roboguru

Perhatikan gambar berikut. Persamaan grafik pada gambar adalah ....

Pertanyaan

Perhatikan gambar berikut.

Persamaan grafik pada gambar adalah ....

  1. begin mathsize 14px style straight y equals log presuperscript 3 space straight x minus 2 end style 

  2. begin mathsize 14px style y equals log presuperscript 3 space left parenthesis 2 x plus 1 right parenthesis minus 2 end style 

  3. begin mathsize 14px style y equals log presuperscript 2 space left parenthesis x plus 4 right parenthesis minus 3 end style 

  4. y equals log presuperscript 2 space x minus 2 

  5. y equals log presuperscript 2 space left parenthesis x minus 2 right parenthesis 

Pembahasan:

Pada gambar di atas, grafik hanya melalui tiga titik maka kita gunakan fungsi begin mathsize 14px style straight y equals log presuperscript straight a left parenthesis bx plus straight c right parenthesis end style .

Grafk melalui titik begin mathsize 14px style left parenthesis 1 comma space minus 2 right parenthesis end style, begin mathsize 14px style left parenthesis 2 comma space minus 1 right parenthesis end style dan begin mathsize 14px style left parenthesis 4 comma space 0 right parenthesis end style. Kita substitusi kedua titik tersebut ke fungsi logaritmanya.

Substitusi titik begin mathsize 14px style left parenthesis 1 comma space minus 2 right parenthesis end style maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight y equals cell log presuperscript straight a left parenthesis bx plus straight c right parenthesis end cell row cell negative 2 end cell equals cell log presuperscript straight a left parenthesis straight b times 1 plus straight c right parenthesis end cell row cell negative 2 end cell equals cell log presuperscript straight a left parenthesis straight b plus straight c right parenthesis end cell row cell straight b plus straight c end cell equals cell straight a to the power of negative 2 end exponent end cell row cell straight b plus straight c end cell equals cell 1 over straight a squared end cell end table end style 

Persamaan i.   

Substitusi titik begin mathsize 14px style left parenthesis 2 comma space minus 1 right parenthesis end style maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight y equals cell log presuperscript straight a left parenthesis bx plus straight c right parenthesis end cell row cell negative 1 end cell equals cell log presuperscript straight a left parenthesis straight b times 2 plus straight c right parenthesis end cell row cell negative 1 end cell equals cell log presuperscript straight a left parenthesis 2 straight b plus straight c right parenthesis end cell row cell 2 straight b plus straight c end cell equals cell straight a to the power of negative 1 end exponent end cell row cell 2 straight b plus straight c end cell equals cell 1 over straight a end cell end table end style 

Persamaan ii

Substitusi titik begin mathsize 14px style left parenthesis 4 comma space 0 right parenthesis end style maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row 0 equals cell log presuperscript straight a left parenthesis straight b times 4 plus straight c right parenthesis end cell row 0 equals cell log presuperscript straight a left parenthesis 4 straight b plus straight c right parenthesis end cell row cell 4 straight b plus straight c end cell equals cell straight a to the power of 0 end cell row cell 4 straight b plus straight c end cell equals 1 end table end style 

Persamaan iii.

eliminasi persamaan i dan ii 

begin mathsize 14px style table row cell straight b plus straight c equals 1 over straight a squared end cell blank row cell 2 straight b plus straight c equals 1 over straight a end cell minus row cell negative straight b equals 1 over straight a squared minus 1 over straight a end cell blank row cell negative straight b equals 1 over straight a left parenthesis 1 over straight a minus 1 right parenthesis end cell blank row cell straight b equals 1 over straight a left parenthesis 1 minus 1 over straight a right parenthesis end cell blank end table end style    

dari persamaan ii kita substitusikan nilai begin mathsize 14px style b end style maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight b plus straight c end cell equals cell 1 over straight a end cell row cell 2 left parenthesis 1 over straight a left parenthesis 1 minus 1 over straight a right parenthesis right parenthesis plus straight c end cell equals cell 1 over straight a end cell row cell 2 over straight a left parenthesis 1 minus 1 over straight a right parenthesis plus straight c end cell equals cell 1 over straight a end cell row straight c equals cell 1 over straight a minus 2 over straight a left parenthesis 1 minus 1 over straight a right parenthesis end cell row blank equals cell 1 over straight a minus 2 over straight a plus 2 over straight a squared end cell row blank equals cell negative 1 over straight a plus 2 over straight a squared end cell row blank equals cell 1 over straight a left parenthesis 2 over straight a minus 1 right parenthesis end cell end table end style 

Dari persamaan iii substitusi nilai begin mathsize 14px style a space dan space b end style maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 straight b plus straight c end cell equals 1 row cell 4 times 1 over straight a left parenthesis 1 minus 1 over straight a right parenthesis plus 1 over straight a left parenthesis 2 over straight a minus 1 right parenthesis end cell equals 1 row cell 4 over straight a left parenthesis 1 minus 1 over straight a right parenthesis plus 2 over straight a squared minus 1 over straight a end cell equals 1 row cell 4 over straight a minus 4 over straight a squared plus 2 over straight a squared minus 1 over straight a end cell equals 1 row cell straight a squared left parenthesis 4 over straight a minus 4 over straight a squared plus 2 over straight a squared minus 1 over straight a right parenthesis end cell equals cell 1 times straight a squared end cell row cell 4 straight a minus 4 plus 2 minus straight a end cell equals cell straight a squared end cell row cell 3 straight a minus 2 end cell equals cell straight a squared end cell row cell negative straight a squared plus 3 straight a minus 2 end cell equals 0 row cell straight a squared minus 3 straight a plus 2 end cell equals 0 row cell left parenthesis straight a minus 2 right parenthesis left parenthesis straight a minus 1 right parenthesis end cell equals 0 row a equals cell 2 space end cell row blank blank cell a t a u end cell row a equals 1 end table end style 

Karena syarat basis tidak sama dengan 1 maka begin mathsize 14px style a equals 2 end style yang memenuhi.

Menentukan nilai begin mathsize 14px style b end style dan begin mathsize 14px style c. end style  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight b equals cell 1 over straight a left parenthesis 1 minus 1 over straight a right parenthesis end cell row blank equals cell 1 half left parenthesis 1 minus 1 half right parenthesis end cell row blank equals cell 1 half left parenthesis 1 half right parenthesis end cell row blank equals cell 1 fourth end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row c equals cell 1 over straight a left parenthesis 2 over straight a minus 1 right parenthesis end cell row blank equals cell 1 half left parenthesis 2 over 2 minus 1 right parenthesis end cell row blank equals 0 end table end style 

Kesimpulan: Fungsi logaritma dari grafik di atas adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight y equals cell log presuperscript straight a left parenthesis bx plus straight c right parenthesis end cell row blank equals cell log presuperscript 2 left parenthesis 1 fourth straight x plus 0 right parenthesis end cell row blank equals cell log presuperscript 2 left parenthesis 1 fourth straight x right parenthesis end cell row blank equals cell log presuperscript 2 left parenthesis 2 to the power of negative 2 end exponent straight x right parenthesis end cell row blank equals cell log presuperscript 2 space 2 to the power of negative 2 end exponent plus log presuperscript 2 space straight x end cell row blank equals cell negative 2 plus log presuperscript 2 space straight x end cell row blank equals cell log presuperscript 2 space straight x minus 2 end cell end table end style 

Jadi, Fungsi logaritma dari grafik di atas adalah Error converting from MathML to accessible text. 

Oleh karena itu, Jawaban yang benar adalah D

Jawaban terverifikasi

Dijawab oleh:

Terakhir diupdate 11 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan serupa

Grafik fungsi f(x)=alogbx melalui titik (4,−3). Grafik fungsi g(x) merupakan hasil pergeseran fungsi f(x) ke bawah dua satuan. Jika grafik fungsi  melalui titik (1,−3). Tentukan persamaan grafik fungs...

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

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

Ikuti Kami

©2021 Ruangguru. All Rights Reserved