Pertanyaan

Jika 8 x x − 3 2 = 4 1 maka nilai dari 3 − x = ...

Jika $\frac{2}{8 ^{\frac{x - 3}{x}}} = \frac{1}{4}$ maka nilai dari $3^{- x} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A

Pembahasan

Ingat kembali: Pertama kita ubah: Sehingga diperoleh perhitungan: maka, Jadi, hasil nilai dari adalah Jadi, jawaban yang tepat adalah A

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 m over a to the power of n equals a to the power of m minus n end exponent comma space a not equal to 0

n-th root of a equals a to the power of 1 over n end exponent comma a space dan space n 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:

4 equals 2 cross times 2 equals 2 squared

8 equals 2 cross times 2 cross times 2 equals 2 cubed

Sehingga diperoleh perhitungan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 over denominator square root of 8 to the power of fraction numerator x minus 3 over denominator x end fraction end exponent end root end fraction end cell equals cell 1 fourth end cell row cell fraction numerator 2 over denominator square root of open parentheses 2 cubed close parentheses to the power of fraction numerator x minus 3 over denominator x end fraction end exponent end root end fraction end cell equals cell 1 over 2 squared end cell row cell fraction numerator 2 over denominator square root of 2 to the power of 3 open parentheses fraction numerator x minus 3 over denominator x end fraction close parentheses end exponent end root end fraction end cell equals cell 2 to the power of negative 2 end exponent end cell row cell fraction numerator 2 over denominator square root of 2 to the power of fraction numerator 3 x minus 9 over denominator x end fraction end exponent end root end fraction end cell equals cell 2 to the power of negative 2 end exponent end cell row cell 2 over 2 to the power of begin display style 1 half end style open parentheses fraction numerator 3 x minus 9 over denominator x end fraction close parentheses end exponent end cell equals cell 2 to the power of negative 2 end exponent end cell row cell 2 over 2 to the power of begin display style fraction numerator 3 x minus 9 over denominator 2 x end fraction end style end exponent end cell equals cell 2 to the power of negative 2 end exponent end cell row cell 2 to the power of 1 minus fraction numerator 3 x minus 9 over denominator 2 x end fraction end exponent end cell equals cell 2 to the power of negative 2 end exponent end cell row cell 2 to the power of fraction numerator 2 x minus 3 x plus 9 over denominator 2 x end fraction end exponent end cell equals cell 2 to the power of negative 2 end exponent end cell row cell 2 to the power of fraction numerator negative x plus 9 over denominator 2 x end fraction end exponent end cell equals cell 2 to the power of negative 2 end exponent comma space sehingga end cell row cell fraction numerator negative straight x plus 9 over denominator 2 straight x end fraction end cell equals cell negative 2 end cell row cell negative straight x plus 9 end cell equals cell negative 2 times 2 straight x end cell row cell negative straight x plus 9 end cell equals cell negative 4 straight x end cell row cell negative straight x plus 4 straight x end cell equals cell negative 9 end cell row cell 3 straight x end cell equals cell negative 9 end cell row straight x equals cell negative 9 over 3 end cell row straight x equals cell negative 3 end cell end table$

maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of negative x end exponent end cell equals cell 3 to the power of negative open parentheses negative 3 close parentheses end exponent end cell row blank equals cell 3 cubed end cell row blank equals 27 end table

Jadi, hasil nilai dari 3 to the power of negative x end exponent adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 27 end table

Jadi, jawaban yang tepat adalah A