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Pertanyaan

Jika 2 to the power of 3 x plus 1 end exponent equals 5, maka x equals horizontal ellipsis

  1. scriptbase log invisible function application 5 end scriptbase presuperscript 2 minus 1

  2. 1 half open parentheses scriptbase log invisible function application 5 end scriptbase presuperscript 2 minus 1 close parentheses

  3. 1 third open parentheses scriptbase log invisible function application 5 end scriptbase presuperscript 2 minus 1 close parentheses

  4. scriptbase log invisible function application 5 end scriptbase presuperscript 2 plus 1

  5. 1 half open parentheses scriptbase log invisible function application 5 end scriptbase presuperscript 2 plus 1 close parentheses

Pembahasan Soal:

Ingat sifat-sifat pada bentuk logaritma yaitu 

  • scriptbase log invisible function application f left parenthesis x right parenthesis end scriptbase presuperscript a equals scriptbase log invisible function application b end scriptbase presuperscript a rightwards arrow f open parentheses x close parentheses equals b
  • scriptbase log invisible function application b to the power of m end scriptbase presuperscript a equals m times scriptbase log invisible function application b end scriptbase presuperscript a
  • fraction numerator scriptbase log invisible function application b end scriptbase presuperscript a over denominator scriptbase log invisible function application c end scriptbase presuperscript a end fraction equals scriptbase log invisible function application b end scriptbase presuperscript c

Sehingga akan diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of 3 x plus 1 end exponent end cell equals 5 row cell log invisible function application 2 to the power of 3 x plus 1 end exponent end cell equals cell log invisible function application 5 end cell row cell left parenthesis 3 x plus 1 right parenthesis log invisible function application 2 end cell equals cell log invisible function application 5 end cell row cell 3 x plus 1 end cell equals cell fraction numerator log invisible function application 5 over denominator log invisible function application 2 end fraction end cell row cell 3 x plus 1 end cell equals cell scriptbase log invisible function application 5 end scriptbase presuperscript 2 end cell row cell 3 x end cell equals cell scriptbase log invisible function application 5 end scriptbase presuperscript 2 minus 1 end cell row x equals cell fraction numerator scriptbase log invisible function application 5 end scriptbase presuperscript 2 minus 1 over denominator 3 end fraction end cell row x equals cell 1 third open parentheses scriptbase log invisible function application 5 end scriptbase presuperscript 2 minus 1 close parentheses end cell end table

Jadi, dapat disimpulkan bahwa jika 2 to the power of 3 x plus 1 end exponent equals 5, maka x equals 1 third open parentheses scriptbase log invisible function application 5 end scriptbase presuperscript 2 minus 1 close parentheses.

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Iqbal

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 11 Juli 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika  maka

Pembahasan Soal:

Logaritma merupakan invers dari eksponen.

Jika a to the power of p equals b maka log presuperscript a space b equals p 

Ingat kembali sifat bentuk logaritma berikut ini.

 log presuperscript a space b equals fraction numerator log presuperscript p space b over denominator log presuperscript p space a end fraction comma space p not equal to 1  

log presuperscript a space open parentheses b to the power of m close parentheses equals m open parentheses log presuperscript a space b close parentheses 

Dengan definisi dan sifat bentuk logaritma di atas, diperoleh perhitungan berikut ini.

     table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space x times log presuperscript 5 space 4 end cell equals 6 row cell log presuperscript 2 space x times log presuperscript 5 space 2 squared end cell equals 6 row cell log presuperscript 2 space x times 2 space open parentheses log presuperscript 5 space 2 close parentheses end cell equals 6 row cell 1 half times 2 times fraction numerator log space x over denominator up diagonal strike log space 2 end strike end fraction times fraction numerator up diagonal strike log space 2 end strike over denominator log space 5 end fraction end cell equals cell 1 half times 6 end cell row cell fraction numerator log space x over denominator log space 5 end fraction end cell equals 3 row cell scriptbase log space x end scriptbase presuperscript 5 end cell equals 3 row x equals cell 5 cubed end cell end table  

Jadi, jawaban yang tepat adalah C.

Roboguru

apabila

Pembahasan Soal:

Ingat sifat pada persamaan bentuk logaritma yaitu scriptbase log invisible function application f left parenthesis x right parenthesis end scriptbase presuperscript a equals scriptbase log invisible function application g left parenthesis x right parenthesis end scriptbase presuperscript b rightwards arrow f open parentheses x close parentheses equals g left parenthesis x right parenthesis dan sifat pada bentuk logaritma yaitu fraction numerator scriptbase log invisible function application b end scriptbase presuperscript a over denominator scriptbase log invisible function application c end scriptbase presuperscript a end fraction equals scriptbase log invisible function application b end scriptbase presuperscript c. Ingat syarat basis pada logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu a greater than 0 dan a not equal to 1 dan syarat numerus pada logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu b greater than 0. Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application open parentheses x squared plus 1 close parentheses end scriptbase presuperscript 3 times scriptbase log invisible function application 3 end scriptbase presuperscript 5 end cell equals cell scriptbase log invisible function application open parentheses x plus 21 close parentheses end scriptbase presuperscript 5 end cell row cell scriptbase log invisible function application left parenthesis x squared plus 1 right parenthesis end scriptbase presuperscript 3 end cell equals cell fraction numerator scriptbase log invisible function application left parenthesis x plus 21 right parenthesis end scriptbase presuperscript 5 over denominator scriptbase log invisible function application 3 end scriptbase presuperscript 5 end fraction end cell row cell scriptbase log invisible function application left parenthesis x squared plus 1 right parenthesis end scriptbase presuperscript 3 end cell equals cell scriptbase log invisible function application left parenthesis x plus 21 right parenthesis end scriptbase presuperscript 3 end cell row cell x squared plus 1 end cell equals cell x plus 21 end cell row cell x squared plus 1 minus x minus 21 end cell equals 0 row cell x squared minus x minus 20 end cell equals 0 row cell left parenthesis x minus 5 right parenthesis left parenthesis x plus 4 right parenthesis end cell equals 0 row cell x minus 5 end cell equals cell 0 blank atau blank x plus 4 equals 0 end cell row x equals cell 5 blank atau blank x equals negative 4 end cell end table

Didapatkan nilai x yaitu x equals 5 dan x equals negative 4, kedua nilai tersebut memenuhi syarat basis dan numerus pada bentuk logaritma jika di substitusikan ke persamaannya. 

Jadi, dapat disimpulkan bahwa scriptbase log invisible function application left parenthesis x squared plus 1 right parenthesis end scriptbase presuperscript 3 times scriptbase log invisible function application 3 end scriptbase presuperscript 5 equals scriptbase log invisible function application left parenthesis x plus 21 right parenthesis end scriptbase presuperscript 5 apabila nilai x yaitu x equals 5 dan x equals negative 4.

Oleh karena itu, jawaban yang benar adalah E.

Roboguru

Jika  maka ...

Pembahasan Soal:

Diketahui : 3 to the power of 2 x minus 1 end exponent equals 6 to the power of x times 3 to the power of 1 minus x end exponent

Ingat kembali bahwa :

bullet space left parenthesis ab right parenthesis to the power of straight m equals straight a to the power of straight m straight b to the power of straight m bullet space straight a to the power of straight m straight a to the power of straight n equals straight a to the power of straight m plus straight n end exponent bullet space straight a to the power of straight m over straight a to the power of straight n equals straight a to the power of straight m minus straight n end exponent  

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of 2 x minus 1 end exponent end cell equals cell 6 to the power of x times 3 to the power of 1 minus x end exponent end cell row cell 3 to the power of 2 x minus 1 end exponent end cell equals cell left parenthesis 2 times 3 right parenthesis to the power of x times 3 to the power of 1 minus x end exponent space end cell row cell 3 to the power of 2 x minus 1 end exponent end cell equals cell 2 to the power of x times 3 to the power of x times 3 to the power of 1 minus x end exponent end cell row cell 3 to the power of 2 x minus 1 end exponent end cell equals cell 2 to the power of x times 3 end cell row cell 3 to the power of 2 x minus 1 end exponent over 3 end cell equals cell 2 to the power of x end cell row cell 3 to the power of 2 x minus 2 end exponent end cell equals cell 2 to the power of x end cell end table  

Ubah bentuk eksponen tersebut ke bentuk logaritma

Ingat kembali bahwa : 

bullet space log presuperscript straight a space f left parenthesis x right parenthesis equals log presuperscript straight a space g left parenthesis x right parenthesis rightwards arrow f left parenthesis x right parenthesis equals g left parenthesis x right parenthesis bullet space log presuperscript straight a space straight b to the power of straight m equals straight m space log presuperscript straight a space straight b bullet space log presuperscript straight a space straight b minus log presuperscript straight a space straight c equals log presuperscript straight a space straight b over straight c bullet space fraction numerator log presuperscript straight p space straight b over denominator log presuperscript straight p space straight a end fraction equals log presuperscript straight a space straight b  

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of 2 x minus 2 end exponent end cell equals cell 2 to the power of x end cell row cell log space 3 to the power of 2 x minus 2 end exponent end cell equals cell log space 2 to the power of x end cell row cell left parenthesis 2 x minus 2 right parenthesis space log space 3 end cell equals cell x space log space 2 end cell row cell 2 x space log space 3 minus 2 space log space 3 end cell equals cell x space log space 2 end cell row cell 2 x space log space 3 minus x space log space 2 end cell equals cell 2 space log space 3 end cell row cell x left parenthesis 2 space log space 3 minus log space 2 right parenthesis end cell equals cell 2 space log space 3 end cell row cell x left parenthesis log space 3 squared minus log space 2 right parenthesis end cell equals cell log space 3 squared end cell row cell x left parenthesis log space 3 squared over 2 right parenthesis end cell equals cell log space 3 squared end cell row cell x left parenthesis log space 9 over 2 right parenthesis end cell equals cell log space 9 end cell row x equals cell fraction numerator log space 9 over denominator log space begin display style 9 over 2 end style end fraction end cell row x equals cell fraction numerator log space 9 over denominator log space 4 comma 5 end fraction end cell row x equals cell log presuperscript 4 comma 5 end presuperscript space 9 end cell end table 

Oleh karena itu, jawaban yang benar adalah D.

Roboguru

Jika  maka

Pembahasan Soal:

Ingat bentuk umum atau definisi dari logaritma yaitu scriptbase log invisible function application b end scriptbase presuperscript a equals c rightwards arrow a to the power of c equals b dan sifat pada logaritma yaitu

  • scriptbase log invisible function application a end scriptbase presuperscript a equals 1
  • scriptbase log invisible function application b end scriptbase presuperscript a plus scriptbase log invisible function application c end scriptbase presuperscript a equals scriptbase log invisible function application b c end scriptbase presuperscript a
  • fraction numerator 1 over denominator scriptbase log invisible function application b end scriptbase presuperscript a end fraction equals scriptbase log invisible function application a end scriptbase presuperscript b

Maka perhitungannya sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application left parenthesis x squared minus 7 right parenthesis end scriptbase presuperscript 2 end cell equals cell fraction numerator 1 over denominator scriptbase log invisible function application b c end scriptbase presuperscript a plus 1 end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a c end scriptbase presuperscript b plus 1 end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b end scriptbase presuperscript c plus 1 end fraction end cell row blank equals cell fraction numerator 1 over denominator scriptbase log invisible function application b c end scriptbase presuperscript a plus scriptbase log invisible function application a end scriptbase presuperscript a end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a c end scriptbase presuperscript b plus scriptbase log invisible function application b end scriptbase presuperscript b end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b end scriptbase presuperscript c plus scriptbase log invisible function application c end scriptbase presuperscript c end fraction end cell row blank equals cell fraction numerator 1 over denominator scriptbase log invisible function application a b c end scriptbase presuperscript a end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b c end scriptbase presuperscript b end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b c end scriptbase presuperscript c end fraction end cell row blank equals cell scriptbase log invisible function application a end scriptbase presuperscript a b c end presuperscript plus scriptbase log invisible function application b end scriptbase presuperscript a b c end presuperscript plus scriptbase log invisible function application c end scriptbase presuperscript a b c end presuperscript end cell row blank equals cell scriptbase log invisible function application a b c end scriptbase presuperscript a b c end presuperscript end cell row blank equals 1 end table

Didapatkan scriptbase log invisible function application left parenthesis x squared minus 7 right parenthesis end scriptbase presuperscript 2 equals 1, sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application open parentheses x squared minus 7 close parentheses end scriptbase presuperscript 2 end cell equals 1 row cell 2 to the power of 1 end cell equals cell x squared minus 7 end cell row 2 equals cell x squared minus 7 end cell row cell 2 plus 7 end cell equals cell x squared end cell row 9 equals cell x squared end cell row cell square root of 9 end cell equals x row cell plus-or-minus 3 end cell equals x end table

Jadi, dapat disimpulkan bahwa jika scriptbase log invisible function application left parenthesis x squared minus 7 right parenthesis end scriptbase presuperscript 2 equals fraction numerator 1 over denominator scriptbase log invisible function application b c end scriptbase presuperscript a plus 1 end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a c end scriptbase presuperscript b plus 1 end fraction plus fraction numerator 1 over denominator scriptbase log invisible function application a b end scriptbase presuperscript c plus 1 end fraction maka blank x equals plus-or-minus 3.

Oleh karena itu, jawaban yang benar adalah E.

Roboguru

Nilai yang memenuhi persamaan  adalah ...

Pembahasan Soal:

Ingat sifat pada persamaan bentuk logaritma yaitu scriptbase log invisible function application f left parenthesis x right parenthesis end scriptbase presuperscript a equals scriptbase log invisible function application g left parenthesis x right parenthesis end scriptbase presuperscript b rightwards arrow f open parentheses x close parentheses equals g left parenthesis x right parenthesis dan sifat pada bentuk logaritma yaitu 

  • scriptbase log invisible function application a end scriptbase presuperscript a equals 1
  • scriptbase log invisible function application b to the power of m end scriptbase presuperscript a equals m times scriptbase log invisible function application b end scriptbase presuperscript a
  • scriptbase log invisible function application b end scriptbase presuperscript a minus scriptbase log invisible function application c end scriptbase presuperscript a equals scriptbase log invisible function application b over c end scriptbase presuperscript a

Ingat syarat basis pada logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu a greater than 0 dan a not equal to 1 dan syarat numerus pada logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu b greater than 0. Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application open parentheses x plus 6 close parentheses end scriptbase presuperscript x end cell equals cell 4 times scriptbase log invisible function application 2 end scriptbase presuperscript x minus 1 end cell row cell scriptbase log invisible function application left parenthesis x plus 6 right parenthesis end scriptbase presuperscript x end cell equals cell scriptbase log invisible function application 2 to the power of 4 end scriptbase presuperscript x minus scriptbase log invisible function application x end scriptbase presuperscript x end cell row cell scriptbase log invisible function application left parenthesis x plus 6 right parenthesis end scriptbase presuperscript x end cell equals cell scriptbase log invisible function application 16 end scriptbase presuperscript x minus scriptbase log invisible function application x end scriptbase presuperscript x end cell row cell scriptbase log invisible function application left parenthesis x plus 6 right parenthesis end scriptbase presuperscript x end cell equals cell scriptbase log invisible function application open parentheses 16 over x close parentheses end scriptbase presuperscript x end cell row cell x plus 6 end cell equals cell 16 over x end cell row cell x open parentheses x plus 6 close parentheses end cell equals 16 row cell x squared plus 6 x end cell equals 16 row cell x squared plus 6 x minus 16 end cell equals 0 row cell left parenthesis x minus 2 right parenthesis left parenthesis x plus 8 right parenthesis end cell equals 0 row cell x minus 2 end cell equals cell 0 blank atau blank x plus 8 equals 0 end cell row x equals cell 2 blank atau blank x equals negative 8 end cell end table

Didapatkan nilai x yaitu 2 dan negative 8. Berdasarkan pada syarat basis dan numerus pada bentuk logaritma maka x yang memenuhi hanya x equals 2 blankkarena untuk x equals negative 8 maka basisnya tidak memenuhi syarat.

Jadi, dapat disimpulkan bawa nilai x yang memenuhi persamaan scriptbase log invisible function application left parenthesis x plus 6 right parenthesis end scriptbase presuperscript x equals 4 times scriptbase log invisible function application 2 end scriptbase presuperscript x minus 1 adalah x equals 2 blank.

Oleh karena itu, jawaban yang benar adalah A.

Roboguru

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