Pertanyaan

Akar-akar dari 3 lo g 2 x − 3 ⋅ 3 lo g 2 + 1 = 0 adalah x 1 dan x 2 . Nilai x 1 ⋅ x 2 = ...

Akar-akar dari $^{3} lo g^{2} x - 3 \cdot^{3} lo g^{2} + 1 = 0$ adalah $x_{1} dan x_{2}$ . Nilai $x_{1} \cdot x_{2} = ...$

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D

Pembahasan

Ingat kembali: Jika maka: Misalkan: Sehingga diperoleh perhitungan: Dengan menggunakan rumus ABC kita tentukan akar-akar persamaan di atas: Untuk Untuk Sehingga, Dengan demikian, nilai adalah Jadi, jawaban yang tepat adalah D

Ingat kembali:

Jika f left parenthesis x right parenthesis equals a x squared plus b x plus c maka:

Error converting from MathML to accessible text.

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 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 to the power of b equals c rightwards arrow b equals log presuperscript a space c

log presuperscript a space f open parentheses x close parentheses equals p rightwards arrow f open parentheses x close parentheses equals a to the power of p comma space a not equal to 0

a to the power of m times a to the power of n equals a to the power of m plus n end exponent. 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 log presuperscript 3 superscript 2 space x minus 3 times log presuperscript 3 space x space plus 1 end cell equals 0 row cell a squared minus 3 a plus 1 end cell equals 0 row blank blank cell a equals 1 comma space b equals negative 3 comma space c equals 1 end cell end table

Dengan menggunakan rumus ABC kita tentukan akar-akar persamaan di atas:

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row cell a subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative open parentheses negative 3 close parentheses plus-or-minus square root of open parentheses negative 3 close parentheses squared minus 4 open parentheses 1 close parentheses open parentheses 1 close parentheses end root over denominator 2 open parentheses 1 close parentheses end fraction end cell row cell a subscript 1 comma 2 end subscript end cell equals cell fraction numerator 3 plus-or-minus square root of 9 minus 4 end root over denominator 2 end fraction end cell row cell a subscript 1 end cell equals cell fraction numerator 3 plus square root of 9 minus 4 end root over denominator 2 end fraction end cell row cell a subscript 2 end cell equals cell fraction numerator 3 minus square root of 9 minus 4 end root over denominator 2 end fraction end cell end table$

Untuk Error converting from MathML to accessible text.

$table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log space x end scriptbase presuperscript 3 end cell equals cell fraction numerator 3 plus square root of 5 over denominator 2 end fraction end cell row cell log presuperscript 3 space x end cell equals cell log presuperscript 3 space 3 to the power of fraction numerator 3 plus square root of 5 over denominator 2 end fraction end exponent end cell row cell x subscript 1 end cell equals cell 3 blank to the power of fraction numerator 3 plus square root of 5 over denominator 2 end fraction end exponent end cell end table$

Untuk $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a subscript 2 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 minus square root of 5 over denominator 2 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell scriptbase log space x end scriptbase presuperscript 3 end cell equals cell fraction numerator 3 minus square root of 5 over denominator 2 end fraction end cell row cell log presuperscript 3 space x end cell equals cell log presuperscript 3 space 3 to the power of fraction numerator 3 minus square root of 5 over denominator 2 end fraction end exponent end cell row cell x subscript 2 end cell equals cell 3 to the power of fraction numerator 3 minus square root of 5 over denominator 2 end fraction end exponent end cell end table$

Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times straight x subscript 2 end cell equals cell 3 to the power of fraction numerator 3 plus square root of 5 over denominator 2 end fraction end exponent times 3 to the power of fraction numerator 3 minus square root of 5 over denominator 2 end fraction end exponent end cell row blank equals cell 3 to the power of fraction numerator 3 plus square root of 5 over denominator 2 end fraction plus fraction numerator 3 minus square root of 5 over denominator 2 end fraction end exponent end cell row blank equals cell 3 to the power of 6 over 2 end exponent end cell row blank equals cell 3 cubed end cell row blank equals 27 end table$

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

Jadi, jawaban yang tepat adalah D