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Akar-akar dari  2log2x−8⋅2logx​+2=0  adalah x1​danx2​. Nilai x1​⋅x2​=...

Pertanyaan

Akar-akar dari  log presuperscript 2 superscript 2 space x minus 8 times log presuperscript 2 space square root of x plus 2 equals 0  adalah x subscript 1 space dan space straight x subscript 2. Nilai x subscript 1 times x subscript 2 equals...

  1. 4 space

  2. 2 space

  3. 8 space

  4. 16 space

  5. 64 space

Pembahasan Soal:

Ingat kembali:

a to the power of n equals stack stack a cross times a cross times a cross times... cross times a with underbrace below with a space s e b a n y a k space n below comma space a not equal to 0

log presuperscript a space a to the power of n equals n comma space a greater than 0

log presuperscript a space b to the power of n equals n log presuperscript a space b space comma space a space dan space b greater than 0

log presuperscript a space f open parentheses x close parentheses equals log presuperscript a space g open parentheses x close parentheses rightwards arrow f open parentheses x close parentheses equals g open parentheses x close parentheses

a-th root of b to the power of f open parentheses x close parentheses end exponent end root equals b to the power of fraction numerator f open parentheses x close parentheses over denominator a end fraction end exponent comma space b greater than 0

Misalkan:

log presuperscript 2 space x equals a

Sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 superscript 2 space x minus 8 times log presuperscript 2 space square root of x plus 2 end cell equals 0 row cell open parentheses log presuperscript 2 space x close parentheses squared minus 8 times log presuperscript 2 space x to the power of 1 half end exponent plus 2 end cell equals 0 row cell open parentheses log presuperscript 2 space x close parentheses squared minus 8 times 1 half space log presuperscript 2 space x plus 2 end cell equals 0 row cell open parentheses log presuperscript 2 space x close parentheses squared minus 4 space log presuperscript 2 space x plus 2 end cell equals 0 row cell a squared minus 4 a plus 2 end cell equals cell 0 space open parentheses difaktorkan close parentheses end cell row cell open parentheses a minus 2 close parentheses open parentheses a minus 2 close parentheses end cell equals 0 row a equals 2 end table    

Untuk a equals 2 

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space x end cell equals a row cell log presuperscript 2 space x end cell equals 2 row cell log presuperscript 2 space x end cell equals cell log presuperscript 2 space 2 squared end cell row x equals 4 end table  

Karena hanya memeiliki satu penyelesaian, maka x subscript 1 equals x subscript 2 equals 4, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x subscript 2 end cell equals cell 4 times 4 end cell row blank equals 16 end table

Dengan demikian, nilai Error converting from MathML to accessible text.  adalah 16

Jadi, jawaban yang tepat adalah D

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Nasrullah

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Akar-akar dari  2log2x−152log3x​+6=0 adalah x1​danx2​. Nilai x1​+x2​=...

Pembahasan Soal:

Ingat kembali:

a to the power of n equals stack stack a cross times a cross times a cross times... cross times a with underbrace below with a space s e b a n y a k space n below comma space a not equal to 0

log presuperscript a space a to the power of n equals n comma space a greater than 0

log presuperscript a space b to the power of n equals n log presuperscript a space b space comma space a space dan space b greater than 0

a-th root of b to the power of f open parentheses x close parentheses end exponent end root equals b to the power of fraction numerator f open parentheses x close parentheses over denominator a end fraction end exponent comma space b greater than 0

Misalkan:

log presuperscript 2 space x equals a

Sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 superscript 2 space x minus 15 space log presuperscript 2 space cube root of x plus 6 end cell equals 0 row cell open parentheses log presuperscript 2 space x close parentheses squared minus 15 space log presuperscript 2 space x to the power of 1 third end exponent plus 6 end cell equals 0 row cell open parentheses log presuperscript 2 space x close parentheses squared minus 15 space times 1 third times log presuperscript 2 space x plus 6 end cell equals 0 row cell open parentheses log presuperscript 2 space x close parentheses squared minus 5 times log presuperscript 2 space x plus 6 end cell equals 0 row cell a squared minus 5 a plus 6 end cell equals cell 0 space open parentheses difaktorkan close parentheses end cell row cell open parentheses a minus 2 close parentheses open parentheses a minus 3 close parentheses end cell equals 0 row blank blank cell a equals 2 space atau space a equals 3 end cell end table

Untuk a equals 2

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space x end cell equals a row cell log presuperscript 2 space x end cell equals 2 row cell log presuperscript 2 space x end cell equals cell log presuperscript 2 space 2 squared end cell row x equals cell 2 squared end cell row x equals 4 end table

Untuk a equals 3

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space x end cell equals a row cell log presuperscript 2 space x end cell equals 3 row cell log presuperscript 2 space x end cell equals cell log presuperscript 2 space 2 cubed end cell row x equals cell 2 cubed end cell row x equals 8 end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus straight x subscript 2 end cell equals cell 4 plus 8 end cell row blank equals 12 end table

Dengan demikian, nilai Error converting from MathML to accessible text. adalah 12

Jadi, jawaban yang tepat adalah E

0

Roboguru

Akar-akar dari  (4logx−3)4logx=4log161​  adalah x1​danx2​. Nilai x1​⋅x2​=...

Pembahasan Soal:

Ingat kembali:

a to the power of n equals stack stack a cross times a cross times a cross times... cross times a with underbrace below with a space s e b a n y a k space n below comma space a not equal to 0

1 over a to the power of n equals a to the power of negative n end exponent. space a not equal to 0

log presuperscript a space a to the power of n equals n comma space a greater than 0

log presuperscript a space b to the power of n equals n log presuperscript a space b space comma space a space dan space b greater than 0

log presuperscript a space f open parentheses x close parentheses equals log presuperscript a space g open parentheses x close parentheses rightwards arrow f open parentheses x close parentheses equals g open parentheses x close parentheses

Misalkan:

log presuperscript 4 space x equals a

Sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses log presuperscript 4 space x minus 3 close parentheses log presuperscript 4 space x end cell equals cell log presuperscript 4 space 1 over 16 end cell row cell open parentheses log presuperscript 4 space x close parentheses squared minus 3 log presuperscript 4 space x end cell equals cell log presuperscript 4 space 1 over 4 squared end cell row cell open parentheses log presuperscript 4 space x close parentheses squared minus 3 log presuperscript 4 space x end cell equals cell log presuperscript 4 space 4 to the power of negative 2 end exponent end cell row cell open parentheses log presuperscript 4 space x close parentheses squared minus 3 log presuperscript 4 space x end cell equals cell negative 2 end cell row cell open parentheses log presuperscript 4 space x close parentheses squared minus 3 log presuperscript 4 space x plus 2 end cell equals 0 row cell a squared minus 3 a plus 2 end cell equals cell 0 space open parentheses difaktorkan close parentheses end cell row cell open parentheses a minus 1 close parentheses open parentheses a minus 2 close parentheses end cell equals 0 row blank blank cell a equals 1 space atau space a equals 2 end cell end table 

Untuk a equals 1

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 4 space x end cell equals 1 row cell log presuperscript 4 space x end cell equals cell log presuperscript 4 space 4 end cell row x equals 4 end table

Untuk a equals 2

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 4 space x end cell equals 2 row cell log presuperscript 4 space x end cell equals cell log presuperscript 4 space 4 squared end cell row x equals cell 4 squared end cell row x equals 16 end table 

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times straight x subscript 2 end cell equals cell 2 times 16 end cell row blank equals 64 end table 

Dengan demikian, nilai x subscript 1 times x subscript 2  adalah 64

Jadi, jawaban yang tepat adalah A

0

Roboguru

Nilai x yang memenuhi persamaan 2log2log(3⋅2x+1−8)=1+2logx adalah...

Pembahasan Soal:

Ingat kembali:

log presuperscript a space f open parentheses x close parentheses equals log presuperscript a space g open parentheses x close parentheses rightwards arrow f open parentheses x close parentheses equals g open parentheses x close parentheses comma space a greater than 0

a to the power of n equals stack stack a cross times a cross times a cross times... cross times a with underbrace below with a space s e b a n y a k space n below comma space a not equal to 0

 

Sehingga diperoleh perhitungan:

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

Misalkan,

2 to the power of x equals a

Maka diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of 2 x end exponent minus 3 times 2 to the power of x plus 1 end exponent plus 8 end cell equals 0 row cell open parentheses 2 to the power of x close parentheses squared minus 3 times 2 to the power of x times 2 plus 8 end cell equals 0 row cell open parentheses 2 to the power of x close parentheses blank squared minus 6 times 2 blank to the power of x plus 8 end cell equals 0 row cell a squared minus 6 a plus 8 end cell equals cell 0 space open parentheses difaktorkan close parentheses end cell row cell open parentheses a minus 2 close parentheses open parentheses a minus 4 close parentheses end cell equals cell 0 space end cell row blank blank cell straight a equals 2 space atau space straight a equals 4 end cell end table

Untuk a equals 2 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of x end cell equals a row cell 2 to the power of x end cell equals 2 row x equals 1 end table

Untuk a equals 4         

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of x end cell equals a row cell 2 to the power of x end cell equals 4 row cell 2 to the power of x end cell equals cell 2 squared end cell row x equals 2 end table 

Dengan demikian, Himpunan penyelesaian persamaan tersebut adalah 1 dan 2

Jadi, jawaban yang tepat adalah C

0

Roboguru

Akar-akar dari  23logx+3logx3​=5  adalah x1​danx2​. Nilai x12​+x22​=...

Pembahasan Soal:

Ingat kembali:

a to the power of n equals stack stack a cross times a cross times a cross times... cross times a with underbrace below with a space s e b a n y a k space n below comma space a not equal to 0

log presuperscript a space a to the power of n equals n comma space a greater than 0

log presuperscript a space b to the power of n equals n log presuperscript a space b space comma space a space dan space b greater than 0

log presuperscript a space f open parentheses x close parentheses equals log presuperscript a space g open parentheses x close parentheses rightwards arrow f open parentheses x close parentheses equals g open parentheses x close parentheses 

open parentheses a to the power of m close parentheses to the power of n equals a to the power of m times n end exponent comma space a not equal to 0

Misalkan:

log presuperscript 3 space x equals a

Sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 log presuperscript 3 space x plus fraction numerator 3 over denominator log presuperscript 3 space x end fraction end cell equals 5 row cell 2 log presuperscript 3 space x plus fraction numerator 3 over denominator log presuperscript 3 space x end fraction minus 5 end cell equals 0 row cell 2 a plus 3 over a minus 5 end cell equals cell 0 space open parentheses sama minus sama space dikali space straight a close parentheses end cell row cell a open parentheses 2 a close parentheses plus a open parentheses 3 over a close parentheses minus a open parentheses 5 close parentheses end cell equals 0 row cell 2 a squared plus 3 minus 5 a end cell equals 0 row cell 2 a squared minus 5 a plus 3 end cell equals cell 0 space open parentheses difaktorkan close parentheses end cell row cell open parentheses 2 a minus 3 close parentheses open parentheses a minus 1 close parentheses end cell equals 0 row blank blank cell a equals 3 over 2 space text atau  end text a equals 1 end cell end table 

Untuk a equals 1

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 3 space x end cell equals a row cell log presuperscript 3 space x end cell equals 1 row cell log presuperscript 3 space x end cell equals cell log presuperscript 3 space 3 end cell row cell x subscript 1 end cell equals 3 end table  

Untuk a equals 3 over 2

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 3 space x end cell equals a row cell log presuperscript 3 space x end cell equals cell 3 over 2 end cell row cell log presuperscript 3 space x end cell equals cell log presuperscript 3 space 3 to the power of 3 over 2 end exponent end cell row cell x subscript 2 end cell equals cell space 3 to the power of 3 over 2 end exponent end cell end table 

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 squared plus straight x subscript 2 squared end cell equals cell open parentheses 3 close parentheses squared plus open parentheses 3 to the power of 3 over 2 end exponent close parentheses squared end cell row blank equals cell 9 plus 3 to the power of 3 over 2 times 2 end exponent end cell row blank equals cell 9 plus 3 cubed end cell row blank equals cell 9 plus 27 end cell row blank equals 36 end table 

Dengan demikian, nilai x subscript 1 squared plus x subscript 2 squared   adalah 36

Jadi, jawaban yang tepat adalah B

0

Roboguru

Akar-akar dari  12(2logx​)+2logx1​=5 adalah x1​danx2​. Nilai x16​+x26​=...

Pembahasan Soal:

Ingat kembali:

a to the power of n equals stack stack a cross times a cross times a cross times... cross times a with underbrace below with a space s e b a n y a k space n below comma space a not equal to 0

log presuperscript a space a to the power of n equals n comma space a greater than 0

log presuperscript a space b to the power of n equals n log presuperscript a space b space comma space a space dan space b greater than 0

log presuperscript a space f open parentheses x close parentheses equals log presuperscript a space g open parentheses x close parentheses rightwards arrow f open parentheses x close parentheses equals g open parentheses x close parentheses 

open parentheses a to the power of m close parentheses to the power of n equals a to the power of m times n end exponent comma space a not equal to 0

Misalkan:

log presuperscript 2 space x equals a

Sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 12 open parentheses log presuperscript 2 space square root of x close parentheses plus fraction numerator 1 over denominator log presuperscript 2 space x end fraction end cell equals 5 row cell 12 open parentheses log presuperscript 2 space x to the power of 1 half end exponent close parentheses plus fraction numerator 1 over denominator log presuperscript 2 space x end fraction minus 5 end cell equals 0 row cell 12 times 1 half open parentheses log presuperscript 2 space x close parentheses plus fraction numerator 1 over denominator log presuperscript 2 space x end fraction minus 5 end cell equals 0 row cell 6 open parentheses log presuperscript 2 space x close parentheses plus fraction numerator 1 over denominator log presuperscript 2 space x end fraction minus 5 end cell equals 0 row cell 6 straight a plus 1 over straight a minus 5 end cell equals cell 0 space open parentheses sama minus sama space dikali space straight a close parentheses end cell row cell straight a open parentheses 6 straight a close parentheses plus straight a open parentheses 1 over straight a close parentheses minus straight a open parentheses 5 close parentheses end cell equals 0 row cell 6 straight a squared plus 1 minus 5 straight a end cell equals 0 row cell 6 straight a squared minus 5 straight a plus 1 end cell equals cell 0 space open parentheses difaktorkan close parentheses end cell row cell open parentheses 3 straight a minus 1 close parentheses open parentheses 2 straight a minus 1 close parentheses end cell equals 0 row blank blank cell straight a equals 1 third space atau space straight a equals 1 half end cell end table    

Untuk a equals 1 third 

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space x end cell equals a row cell log presuperscript 2 space x end cell equals cell 1 third end cell row cell log presuperscript 2 space x end cell equals cell log presuperscript 2 space 2 to the power of 1 third end exponent end cell row cell x subscript 1 end cell equals cell 2 to the power of 1 third end exponent end cell end table  

Untuk a equals 1 half 

  table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 2 space x end cell equals a row cell log presuperscript 2 space x end cell equals cell 1 half end cell row cell log presuperscript 2 space x end cell equals cell log presuperscript 2 space 2 to the power of 1 half end exponent end cell row cell x subscript 2 end cell equals cell 2 to the power of 1 half end exponent end cell end table 

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 to the power of 6 plus straight x subscript 2 to the power of 6 end cell equals cell open parentheses 2 to the power of 1 third end exponent close parentheses to the power of 6 plus open parentheses 2 to the power of 1 half end exponent close parentheses to the power of 6 end cell row blank equals cell 2 to the power of 1 third times 6 end exponent plus 2 to the power of 1 half times 6 end exponent end cell row blank equals cell 2 squared plus 2 cubed end cell row blank equals cell 4 plus 8 end cell row blank equals 12 end table  

Dengan demikian, nilai x subscript 1 to the power of 6 plus x subscript 2 to the power of 6  adalah 12

Jadi, jawaban yang tepat adalah A

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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

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