Pertanyaan

Jika ( 3 ) x − 2 = ( 27 1 ) x − 2 maka nilai dari 3 x 1 sama dengan...

Jika $(3)^{x - 2} = (\frac{1}{27})^{x - 2}$ maka nilai dari $3^{\frac{1}{x}}$ sama dengan...

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Habis dalam

Klaim

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D

Pembahasan

Ingat kembali: Pertama kita ubah maka, Jadi, hasil nilai dari adalah Jadi, jawaban yang tepat adalah D

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 comma space a not equal to 0

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

a to the power of f open parentheses x close parentheses end exponent equals a to the power of g open parentheses x close parentheses end exponent rightwards arrow f open parentheses x close parentheses equals g open parentheses x close parentheses

Pertama kita ubah 27 equals 3 cross times 3 cross times 3 equals 3 cubed

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 3 close parentheses to the power of x minus 2 end exponent end cell equals cell open parentheses 1 over 27 close parentheses to the power of x minus 2 end exponent end cell row cell open parentheses 3 to the power of 1 half end exponent close parentheses to the power of x minus 2 end exponent end cell equals cell open parentheses 1 over 3 cubed close parentheses to the power of x minus 2 end exponent end cell row cell 3 to the power of 1 half open parentheses x minus 2 close parentheses end exponent end cell equals cell open parentheses 3 to the power of negative 3 end exponent close parentheses to the power of x minus 2 end exponent end cell row cell 3 to the power of 1 half x minus 1 end exponent end cell equals cell 3 to the power of negative 3 open parentheses x minus 2 close parentheses end exponent end cell row cell 3 to the power of 1 half x minus 1 end exponent end cell equals cell 3 to the power of negative 3 x plus 6 end exponent comma space sehingga end cell row cell 1 half x minus 1 end cell equals cell negative 3 x plus 6 end cell row cell 1 half x plus 3 x end cell equals cell 6 plus 1 end cell row cell fraction numerator 7 x over denominator 2 end fraction end cell equals 7 row cell 7 x end cell equals cell 7 times 2 end cell row x equals cell fraction numerator up diagonal strike 7 times 2 over denominator up diagonal strike 7 end fraction end cell row x equals 2 end table$

maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of 1 over x end exponent end cell equals cell 3 to the power of 1 half end exponent end cell row blank equals cell square root of 3 end cell end table

Jadi, hasil nilai dari 3 to the power of 1 over x end exponent adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table

Jadi, jawaban yang tepat adalah D