Pertanyaan

Nilai x yang memenuhi 3 x − 1 27 ≥ 3 2 x + 1 1 adalah...

Nilai x yang memenuhi $\frac{27}{3 ^{x - 1}} \geq \frac{1}{3 ^{2 x + 1}}$ adalah...

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A

Pembahasan

Ingat kembali: Sehingga diperoleh perhitungan: Dengan demikian, Nilai x yang memenuhi 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

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

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

a to the power of f open parentheses x close parentheses end exponent greater or equal than a to the power of g open parentheses x close parentheses end exponent rightwards arrow f open parentheses x close parentheses greater or equal than g open parentheses x close parentheses comma space a greater than 1

$a-th root of b to the power of f open parentheses x close parentheses end exponent end root equals b to the power of fraction numerator f open parentheses x close parentheses over denominator 2 end fraction end exponent comma space b greater than 0$

Sehingga diperoleh perhitungan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 27 over 3 to the power of x minus 1 end exponent end root end cell greater than cell 1 over 3 to the power of 2 x plus 1 end exponent end cell row cell square root of 3 cubed over 3 to the power of x minus 1 end exponent end root end cell greater than cell 3 to the power of negative open parentheses 2 x plus 1 close parentheses end exponent end cell row cell square root of 3 to the power of 3 minus open parentheses x minus 1 close parentheses end exponent end root end cell greater than cell 3 to the power of negative open parentheses 2 x plus 1 close parentheses end exponent end cell row cell square root of 3 to the power of 3 minus x plus 1 end exponent end root end cell greater than cell 3 to the power of negative 2 x minus 1 end exponent end cell row cell square root of 3 to the power of 4 minus x end exponent end root end cell greater than cell 3 to the power of negative 2 x minus 1 end exponent end cell row cell 3 to the power of fraction numerator 4 minus x over denominator 2 end fraction end exponent end cell greater than cell 3 to the power of negative 2 x minus 1 end exponent end cell row cell fraction numerator 4 minus x over denominator 2 end fraction end cell greater than cell negative 2 x minus 1 end cell row cell 4 minus x end cell greater than cell 2 open parentheses negative 2 x minus 1 close parentheses end cell row cell 4 minus x end cell greater than cell negative 4 x minus 2 end cell row cell negative x plus 4 x end cell greater than cell negative 2 minus 4 end cell row cell 3 x end cell greater than cell negative 6 end cell row x greater than cell fraction numerator negative 6 over denominator 3 end fraction end cell row x greater than cell negative 2 end cell end table$

Dengan demikian, Nilai x yang memenuhi adalah x greater than negative 2

Jadi, jawaban yang tepat adalah A