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Pertanyaan

Akar-akar dari  log presuperscript 2 superscript 2 space x minus 15 space log presuperscript 2 space cube root of x plus 6 equals 0 adalah x subscript 1 space dan space straight x subscript 2. Nilai x subscript 1 plus straight x subscript 2 equals...

  1. 3 space

  2. 6 space

  3. 8 space

  4. 9 space

  5. 12 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

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

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Nasrullah

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 12 Juli 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Akar-akar dari    adalah . Nilai

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

Roboguru

Akar-akar dari    adalah . Nilai

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

Roboguru

...

Pembahasan Soal:

Perlu diingat bahwa sifat bentuk logaritma diantaranya adalah log presuperscript a space b to the power of m equals m times log presuperscript a space b dan log presuperscript a space a equals 1 dengan a comma b greater than 0 dan a not equal to 1, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 3 space square root of 3 end cell equals cell log presuperscript 3 space 3 to the power of 1 half end exponent end cell row blank equals cell log presuperscript 3 space 3 to the power of 0 comma 5 end exponent end cell row blank equals cell 0 comma 5 times scriptbase log space 3 end scriptbase presuperscript 3 end cell row blank equals cell 0 comma 5 times 1 end cell row blank equals cell 0 comma 5 end cell end table

Berdasarkan uraian di atas, diperoleh log presuperscript 3 space square root of 3 equals 0 comma 5.

Jadi, jawaban yang tepat adalah C.

Roboguru

...

Pembahasan Soal:

Perlu diingat bahwa:

  • a to the power of b times a to the power of c equals a to the power of b plus c end exponent
  • 1 over a to the power of b equals a to the power of negative b end exponent comma space a not equal to 0
  • log presuperscript a space b to the power of m equals m times log presuperscript a space b comma space a comma b greater than 0 space dan space a not equal to 1
  • log presuperscript a space a equals 1 comma space a greater than 0 space dan space a not equal to 1

Dengan menggunakan sifat bilangan berpangkat dan sifat bentuk logaritma di atas, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript 5 space 1 fifth square root of 5 end cell equals cell log presuperscript 5 space 5 to the power of negative 1 end exponent times 5 to the power of 1 half end exponent end cell row blank equals cell log presuperscript 5 space 5 to the power of negative 1 plus 1 half end exponent end cell row blank equals cell log presuperscript 5 space 5 to the power of negative 1 half end exponent end cell row blank equals cell open parentheses negative 1 half close parentheses times log presuperscript 5 space 5 end cell row blank equals cell open parentheses negative 1 half close parentheses times 1 end cell row blank equals cell negative 1 half end cell row blank equals cell negative 0 comma 5 end cell end table

Berdasarkan definisi di atas, diperoleh log presuperscript 5 space 1 fifth square root of 5 equals negative 0 comma 5.

Jadi, jawaban yang tepat adalah D.

Roboguru

Jika  maka .

Pembahasan Soal:

Diketahui a equals 2 to the power of y, akan ditentukan nilai log presuperscript 2 space square root of a.

Gunakan sifat-sifat bentuk logaritma dan eksponen berikut:

table attributes columnalign right center left columnspacing 2px end attributes row cell log presuperscript a space open parentheses b to the power of m close parentheses end cell equals cell m space open parentheses log presuperscript a space b close parentheses end cell row cell log presuperscript a space a end cell equals 1 row cell m-th root of a to the power of n end root end cell equals cell a to the power of n over m end exponent end cell end table

Dengan mensubtitusikan a equals 2 to the power of y pada log presuperscript 2 space square root of a dan menggunakan sifat-sifat di atas dapat diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell log presuperscript 2 space square root of a end cell equals cell log presuperscript 2 space square root of 2 to the power of y end root end cell row blank equals cell log presuperscript 2 space 2 to the power of begin inline style y over 2 end style end exponent end cell row blank equals cell y over 2 space log presuperscript 2 space 2 end cell row blank equals cell y over 2 times 1 end cell row cell log presuperscript 2 space square root of a end cell equals cell 0 comma 5 y end cell end table

Diperoleh bahwa log presuperscript 2 space square root of a equals 0 comma 5 y.

Jadi, jawaban yang tepat adalah A.

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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