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Supaya xlog(x2x2−9​)=1 maka nilai x harus sama dengan ...

Pertanyaan

Supaya scriptbase log invisible function application left parenthesis fraction numerator 2 x squared minus 9 over denominator x end fraction right parenthesis end scriptbase presuperscript x equals 1 maka nilai x harus sama dengan ...

  1. 1

  2. 2

  3. 3

  4. plus-or-minus 2

  5. plus-or-minus 3

Pembahasan Soal:

Ingat bentuk umum atau definisi pada 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 syarat basis pada bentuk logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu a greater than 0 dan a not equal to 1 serta sifat pada bentuk logaritma yaitu scriptbase log invisible function application a end scriptbase presuperscript a equals 1.

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application open parentheses fraction numerator 2 x squared minus 9 over denominator x end fraction close parentheses end scriptbase presuperscript x end cell equals 1 row cell scriptbase log invisible function application left parenthesis 2 x squared minus 9 right parenthesis end scriptbase presuperscript x minus scriptbase log invisible function application x end scriptbase presuperscript x end cell equals 1 row cell scriptbase log invisible function application left parenthesis 2 x squared minus 9 right parenthesis end scriptbase presuperscript x minus 1 end cell equals 1 row cell scriptbase log invisible function application left parenthesis 2 x squared minus 9 right parenthesis end scriptbase presuperscript x end cell equals cell 1 plus 1 end cell row cell scriptbase log invisible function application left parenthesis 2 x squared minus 9 right parenthesis end scriptbase presuperscript x end cell equals 2 row cell x squared end cell equals cell 2 x squared minus 9 end cell row 0 equals cell 2 x squared minus x squared minus 9 end cell row 0 equals cell x squared minus 9 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

Dari hasil di atas didapakan nilai x yaitu 3 atau negative 3. Berdasarkan syarat basis pada logaritma maka nilai x harus lebih dari 0 sehingga nilai x yang memenuhi adalah 3.

Jadi, dapat disimpulkan bahwa supaya scriptbase log invisible function application left parenthesis fraction numerator 2 x squared minus 9 over denominator x end fraction right parenthesis end scriptbase presuperscript x equals 1 maka nilai x harus sama dengan 3.

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Iqbal

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

Akar-akar xlog2=2−xlog(3x−4) adalah x1​ dan x2​ maka x1​⋅x2​=…

Pembahasan Soal:

Ingat sifat pada persamaan bentuk logaritma yaitu scriptbase log invisible function application b end scriptbase presuperscript a equals scriptbase log invisible function application f left parenthesis x right parenthesis end scriptbase presuperscript b rightwards arrow b equals f 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 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 2 end scriptbase presuperscript x end cell equals cell 2 minus scriptbase log invisible function application open parentheses 3 x minus 4 close parentheses end scriptbase presuperscript x end cell row cell scriptbase log invisible function application 2 end scriptbase presuperscript x end cell equals cell 2 times scriptbase log invisible function application x end scriptbase presuperscript x minus scriptbase log invisible function application left parenthesis 3 x minus 4 right parenthesis end scriptbase presuperscript x end cell row cell scriptbase log invisible function application 2 end scriptbase presuperscript x end cell equals cell scriptbase log invisible function application x squared end scriptbase presuperscript x minus scriptbase log invisible function application left parenthesis 3 x minus 4 right parenthesis end scriptbase presuperscript x end cell row cell scriptbase log invisible function application 2 end scriptbase presuperscript x end cell equals cell scriptbase log invisible function application open parentheses fraction numerator x squared over denominator 3 x minus 4 end fraction close parentheses end scriptbase presuperscript x end cell row 2 equals cell fraction numerator x squared over denominator 3 x minus 4 end fraction end cell row cell 2 left parenthesis 3 x minus 4 right parenthesis end cell equals cell x squared end cell row cell 6 x minus 8 end cell equals cell x squared end cell row 0 equals cell x squared minus 6 x plus 8 end cell row 0 equals cell left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis end cell row cell x minus 2 end cell equals cell 0 blank atau blank x minus 4 equals 0 end cell row x equals cell 2 blank atau blank x equals 4 end cell end table

Didapatkan akar-akar persamaan tersebut yaitu x subscript 1 equals 2 dan x subscript 2 equals 4. Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x subscript 2 end cell equals cell 2 times 4 end cell row blank equals 8 end table

Jadi, dapat disimpulkan bahwa hasil dari x subscript 1 times x subscript 2 adalah 8.

Oleh karena itu, jawaban yang benar adalah D.

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Roboguru

Nilai x yang memenuhi persamaan xlog(x+6)=4⋅xlog2−1 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.

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Himpunan penyelesaian persamaan xlog(6x2−8x)=3 adalah ...

Pembahasan Soal:

Ingat bentuk umum atau definisi pada 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 syarat basis pada bentuk logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu a greater than 0 dan a not equal to 1, serta syarat numerus pada bentuk logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu b greater than 0.

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application open parentheses 6 x squared minus 8 x close parentheses end scriptbase presuperscript x end cell equals 3 row cell x cubed end cell equals cell 6 x squared minus 8 x end cell row cell x cubed minus 6 x squared plus 8 x end cell equals 0 row cell x open parentheses x squared minus 6 x plus 8 close parentheses end cell equals 0 row x equals cell 0 blank atau blank x squared minus 6 x plus 8 equals 0 end cell end table

 

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 6 x plus 8 end cell equals 0 row cell left parenthesis x minus 2 right parenthesis left parenthesis x minus 4 right parenthesis end cell equals 0 row cell x minus 2 end cell equals cell 0 blank atau blank x minus 4 equals 0 end cell row x equals cell 2 blank atau blank x equals 4 end cell end table

Berdasarkan hasil di atas serta syarat basis pada logaritma maka didapatkan himpunan penyelesainnya yaitu left curly bracket 2 , 4 right curly bracket.

Jadi, dapat disimpulkan bahwa himpunan penyelesaian persamaan scriptbase log invisible function application left parenthesis 6 x squared minus 8 x right parenthesis end scriptbase presuperscript x equals 3 adalah left curly bracket 2 , 4 right curly bracket.

Oleh karena itu, jawaban yang benar adalah C.

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Roboguru

Akar-akar dari 3log(x+1)=1+9log(x−1) adalah x1​ dan x2​ maka x1​+x2​=…

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

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 left parenthesis x plus 1 right parenthesis end scriptbase presuperscript 3 end cell equals cell 1 plus scriptbase log invisible function application left parenthesis x minus 1 right parenthesis end scriptbase presuperscript 9 end cell row cell scriptbase log invisible function application left parenthesis x plus 1 right parenthesis end scriptbase presuperscript 3 end cell equals cell scriptbase log invisible function application 3 end scriptbase presuperscript 3 plus scriptbase log invisible function application left parenthesis x minus 1 right parenthesis end scriptbase presuperscript 3 squared end presuperscript end cell row cell scriptbase log invisible function application left parenthesis x plus 1 right parenthesis end scriptbase presuperscript 3 end cell equals cell scriptbase log invisible function application 3 end scriptbase presuperscript 3 plus 1 half scriptbase log invisible function application left parenthesis x minus 1 right parenthesis end scriptbase presuperscript 3 end cell row cell scriptbase log invisible function application left parenthesis x plus 1 right parenthesis end scriptbase presuperscript 3 end cell equals cell scriptbase log invisible function application 3 end scriptbase presuperscript 3 plus scriptbase log invisible function application open parentheses left parenthesis x minus 1 right parenthesis to the power of 1 half end exponent close parentheses end scriptbase presuperscript 3 end cell row cell scriptbase log invisible function application left parenthesis x plus 1 right parenthesis end scriptbase presuperscript 3 end cell equals cell scriptbase log invisible function application open parentheses 3 times left parenthesis x minus 1 right parenthesis to the power of 1 half end exponent close parentheses end scriptbase presuperscript 3 end cell row cell x plus 1 end cell equals cell 3 times left parenthesis x minus 1 right parenthesis to the power of 1 half end exponent end cell row cell open parentheses x plus 1 close parentheses squared end cell equals cell open parentheses 3 times left parenthesis x minus 1 right parenthesis to the power of 1 half end exponent close parentheses squared end cell row cell x squared plus 2 x plus 1 end cell equals cell 3 squared times left parenthesis x minus 1 right parenthesis end cell row cell x squared plus 2 x plus 1 end cell equals cell 9 times left parenthesis x minus 1 right parenthesis end cell row cell x squared plus 2 x plus 1 end cell equals cell 9 x minus 9 end cell row cell x squared plus 2 x minus 9 x plus 1 plus 9 end cell equals 0 row cell x squared minus 7 x plus 10 end cell equals 0 row cell left parenthesis x minus 2 right parenthesis left parenthesis x minus 5 right parenthesis end cell equals 0 row cell x minus 2 end cell equals cell 0 blank atau blank x minus 5 equals 0 end cell row x equals cell 2 blank atau blank x equals 5 end cell end table

Didapatkan akar-akar dari persamaan tersebut yaitu x subscript 1 equals 2 dan x equals 5. Maka nilai dari x subscript 1 plus x subscript 2 sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell 2 plus 5 end cell row blank equals 7 end table

Jadi, dapat disimpulkan bahwa nilai dari x subscript 1 plus x subscript 2 adalah 7.

Oleh karena itu, jawaban yang benar adalah D.

0

Roboguru

Nilai x yang memenuhi persamaan xlog(x+2)−3⋅xlog2+1=0  adalah...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript x space open parentheses x plus 2 close parentheses minus 3 times log presuperscript x space 2 plus 1 end cell equals 0 row cell log presuperscript x space open parentheses x plus 2 close parentheses minus log presuperscript x space 2 cubed plus 1 end cell equals 0 row cell log presuperscript x space fraction numerator x plus 2 over denominator 2 cubed end fraction plus 1 end cell equals 0 row cell log presuperscript x space fraction numerator x plus 2 over denominator 8 end fraction end cell equals cell negative 1 end cell row cell fraction numerator x plus 2 over denominator 8 end fraction end cell equals cell x to the power of negative 1 end exponent end cell row cell fraction numerator x plus 2 over denominator 8 end fraction end cell equals cell 1 over x end cell row cell x open parentheses x plus 2 close parentheses end cell equals 8 row cell x squared plus 2 x end cell equals 8 row cell x squared plus 2 x minus 8 end cell equals 0 row cell open parentheses x minus 2 close parentheses open parentheses x plus 4 close parentheses end cell equals 0 row cell x minus 2 end cell equals 0 row x equals 2 row cell x plus 4 end cell equals 0 row x equals cell negative 4 end cell end table 

Jadi, nilai x yang memenuhi adalah x equals 2 space dan space x equals negative 4.

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

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