Roboguru

Nilai dari 2log6+2log8−2log12=....

Pertanyaan

Nilai dari log presuperscript 2 space 6 plus log presuperscript 2 space 8 space minus space log presuperscript 2 space 12 space equals space....

  1. 2

  2. 1

  3. -1

  4. -2

  5. -3

Pembahasan Soal:

Sifat-sifat yang digunakan:

log presuperscript straight a space straight b space space plus space log presuperscript straight a space straight c space equals space log presuperscript straight a space left parenthesis straight b. straight c right parenthesis  log presuperscript straight a space straight b space minus space log presuperscript straight a space straight c space equals space log presuperscript straight a space straight b over straight c  log presuperscript straight a space straight b to the power of straight n equals straight n space log presuperscript straight a space straight b  log presuperscript straight a space straight a space equals space 1    log presuperscript 2 space 6 space plus space log presuperscript 2 space 8 space minus space log presuperscript 2 space 12 space equals space log presuperscript 2 space open parentheses fraction numerator 6.8 over denominator 12 end fraction close parentheses  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space log presuperscript 2 space 4  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space log presuperscript 2 space 2 squared  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 2. space log presuperscript 2 space 2  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 2.1 space  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 2

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Fatimatuzzahroh

Mahasiswa/Alumni Institut Pertanian Bogor

Terakhir diupdate 04 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Nilai dari 2log4+2log12−2log6=....

Pembahasan Soal:

log presuperscript straight a space xy space equals space log presuperscript straight a space straight x plus log presuperscript straight a space straight y  log presuperscript straight a space straight x over straight y space equals space log presuperscript straight a space straight x minus log presuperscript straight a space straight y  log presuperscript 2 space 4 plus space log presuperscript 2 space 12 minus log presuperscript 2 space 6 space equals space log presuperscript 2 space fraction numerator 4.12 over denominator 6 end fraction  equals log presuperscript 2 space 8  equals log presuperscript 2 space 2 cubed  equals 3

0

Roboguru

Bentuk sederhana dari  adalah ...

Pembahasan Soal:

Untuk menyelesaikan soal tersebut ingat sifat-sifat berikut.

  • 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 end scriptbase presuperscript a times scriptbase log invisible function application c end scriptbase presuperscript b equals scriptbase log invisible function application c end scriptbase presuperscript a
  • 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

Sehingga akan didapatkan

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses log invisible function application x close parentheses squared minus open parentheses log invisible function application y close parentheses squared over denominator scriptbase log invisible function application 4 end scriptbase presuperscript 125 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 9 end scriptbase presuperscript 8 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction end cell equals cell fraction numerator left parenthesis log invisible function application x plus log invisible function application y right parenthesis left parenthesis log invisible function application x minus log invisible function application y right parenthesis over denominator scriptbase log invisible function application 2 squared end scriptbase presuperscript 5 cubed end presuperscript times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 3 squared end scriptbase presuperscript 2 cubed end presuperscript times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 scriptbase log invisible function application 2 end scriptbase presuperscript 5 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus 2 over 3 scriptbase log invisible function application 3 end scriptbase presuperscript 2 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 scriptbase log invisible function application 5 end scriptbase presuperscript 5 times log invisible function application x minus 2 over 3 scriptbase log invisible function application 2 end scriptbase presuperscript 2 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 times 1 times log invisible function application x minus 2 over 3 times 1 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 times log invisible function application x minus 2 over 3 times log invisible function application y end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 left parenthesis log invisible function application x minus log invisible function application y right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis log invisible function application left parenthesis x y right parenthesis right parenthesis open parentheses log invisible function application open parentheses x over y close parentheses close parentheses over denominator 2 over 3 open parentheses log invisible function application open parentheses x over y close parentheses close parentheses end fraction end cell row blank equals cell fraction numerator log invisible function application left parenthesis x y right parenthesis over denominator 2 over 3 end fraction end cell row blank equals cell 3 over 2 log invisible function application left parenthesis x y right parenthesis end cell end table end style

Jadi, dapat disimpulkan bahwa bentuk sederhana dari fraction numerator open parentheses log invisible function application x close parentheses squared minus open parentheses log invisible function application y close parentheses squared over denominator scriptbase log invisible function application 4 end scriptbase presuperscript 125 times scriptbase log invisible function application 5 end scriptbase presuperscript 2 times log invisible function application x minus scriptbase log invisible function application 9 end scriptbase presuperscript 8 times scriptbase log invisible function application 2 end scriptbase presuperscript 3 times log invisible function application y end fraction adalah 3 over 2 log invisible function application left parenthesis x y right parenthesis.

Oleh karena itu, jawaban yang benar adalah C.

0

Roboguru

Nilai dari 3.2logy−2logy2+2logy1​=....

Pembahasan Soal:

Ingat space kembali space sifat space logaritma space berikut space ini  squared log space xy space equals squared log space straight x space plus squared log space straight y space  squared log space straight x over straight y equals squared log space straight x space minus squared log space straight y space  Maka space space  3. squared log space straight y minus squared log space straight y squared plus squared log 1 over straight y space space  equals squared log space straight y to the power of 3 space end exponent minus squared log space straight y squared space plus squared log 1 over straight y space space space space  equals squared log space open parentheses fraction numerator straight y cubed cross times begin display style 1 over straight y end style over denominator straight y squared end fraction close parentheses  equals squared log space 1 space space  equals 0 space

0

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 x+1log(2x+5)=2⋅2log122log224−2log26​ adalah ...

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-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 minus scriptbase log invisible function application c end scriptbase presuperscript a equals scriptbase log invisible function application b over c end scriptbase presuperscript a
  • 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 equals m times scriptbase log invisible function application b end scriptbase presuperscript a

serta 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. Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application open parentheses 2 x plus 5 close parentheses end scriptbase presuperscript x plus 1 end presuperscript end cell equals cell fraction numerator scriptbase log squared invisible function application 24 end scriptbase presuperscript 2 minus scriptbase log squared invisible function application 6 end scriptbase presuperscript 2 over denominator 2 times scriptbase log invisible function application 12 end scriptbase presuperscript 2 end fraction end cell row blank equals cell fraction numerator left parenthesis scriptbase log invisible function application 24 end scriptbase presuperscript 2 plus scriptbase log invisible function application 6 end scriptbase presuperscript 2 right parenthesis left parenthesis scriptbase log invisible function application 24 end scriptbase presuperscript 2 minus scriptbase log invisible function application 6 end scriptbase presuperscript 2 right parenthesis over denominator scriptbase log invisible function application 12 squared end scriptbase presuperscript 2 end fraction end cell row blank equals cell fraction numerator open parentheses scriptbase log invisible function application left parenthesis 24 times 6 right parenthesis end scriptbase presuperscript 2 close parentheses open parentheses scriptbase log invisible function application 24 over 6 end scriptbase presuperscript 2 close parentheses over denominator scriptbase log invisible function application 144 end scriptbase presuperscript 2 end fraction end cell row blank equals cell fraction numerator open parentheses scriptbase log invisible function application 144 end scriptbase presuperscript 2 close parentheses open parentheses scriptbase log invisible function application 4 end scriptbase presuperscript 2 close parentheses over denominator scriptbase log invisible function application 144 end scriptbase presuperscript 2 end fraction end cell row blank equals cell scriptbase log invisible function application 4 end scriptbase presuperscript 2 end cell row blank equals cell scriptbase log invisible function application 2 squared end scriptbase presuperscript 2 end cell row blank equals cell 2 times scriptbase log invisible function application 2 end scriptbase presuperscript 2 end cell row blank equals 2 end table

Dari hasil di atas didapatkan scriptbase log invisible function application open parentheses 2 x plus 5 close parentheses end scriptbase presuperscript x plus 1 end presuperscript equals 2, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log invisible function application open parentheses 2 x plus 5 close parentheses end scriptbase presuperscript x plus 1 end presuperscript end cell equals 2 row cell left parenthesis x plus 1 right parenthesis squared end cell equals cell 2 x plus 5 end cell row cell x squared plus 2 x plus 1 end cell equals cell 2 x plus 5 end cell row cell x squared plus 2 x minus 2 x plus 1 minus 5 end cell equals 0 row cell x squared minus 4 end cell equals 0 row cell x squared end cell equals 4 row x equals cell square root of 4 end cell row x equals cell plus-or-minus 2 end cell end table

Didapatkan hasil  nilai x yaitu negative 2 atau 2. Karena syarat basis dari logaritma scriptbase log invisible function application b end scriptbase presuperscript a yaitu a greater than 0 dan a not equal to 1 maka nilai x yang memenuhi adalah x equals 2.

Jadi, dapat disimpulkan bahwa nilai x yang memenuhi persamaan scriptbase log invisible function application left parenthesis 2 x plus 5 right parenthesis end scriptbase presuperscript x plus 1 end presuperscript equals fraction numerator scriptbase log squared invisible function application 24 end scriptbase presuperscript 2 minus scriptbase log squared invisible function application 6 end scriptbase presuperscript 2 over denominator 2 times scriptbase log invisible function application 12 end scriptbase presuperscript 2 end fraction adalah x equals 2.

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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