Nilai x yang memenuhi persamaan 32x+1+32x+2=439x−2 adalah ...

Pertanyaan

Nilai $x$ yang memenuhi persamaan $3^{2x+1}+3^{2x+2}=4\sqrt[3]{9^{x-2}}$ adalah ...

I. Ridha

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C. space

Pembahasan

Ingat kembali:

Jika dengan $a>0$ dan $a\neq1$ , maka
dengan

Oleh karena itu,

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of 2 x plus 1 end exponent plus 3 to the power of 2 x plus 2 end exponent end cell equals cell 4 cube root of 9 to the power of x minus 2 end exponent end root end cell row cell open parentheses 3 times 3 to the power of 2 x end exponent close parentheses plus open parentheses 3 squared times 3 to the power of 2 x end exponent close parentheses end cell equals cell 4 cube root of open parentheses 3 squared close parentheses to the power of x minus 2 end exponent end root end cell row cell 12 times 3 to the power of 2 x end exponent end cell equals cell 4 cube root of 3 to the power of 2 x minus 4 end exponent end root end cell row cell 12 times 3 to the power of 2 x end exponent end cell equals cell 4 times 3 to the power of fraction numerator 2 x minus 4 over denominator 3 end fraction end exponent end cell row cell fraction numerator 12 times 3 to the power of 2 x end exponent over denominator 4 end fraction end cell equals cell 3 to the power of fraction numerator 2 x minus 4 over denominator 3 end fraction end exponent end cell row cell 3 times 3 to the power of 2 x end exponent end cell equals cell 3 to the power of fraction numerator 2 x minus 4 over denominator 3 end fraction end exponent end cell row cell 3 to the power of 2 x plus 1 end exponent end cell equals cell 3 to the power of fraction numerator 2 x minus 4 over denominator 3 end fraction end exponent end cell end table$

sehingga karena $a=3$ yang berarti $a>0$ dan $a\neq1$ , maka diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus 1 end cell equals cell fraction numerator 2 x minus 4 over denominator 3 end fraction end cell row cell 3 cross times open parentheses 2 x plus 1 close parentheses end cell equals cell 2 x minus 4 end cell row cell 6 x plus 3 end cell equals cell 2 x minus 4 end cell row cell 6 x end cell equals cell 2 x minus 4 minus 3 end cell row cell 6 x minus 2 x end cell equals cell negative 4 minus 3 end cell row cell 4 x end cell equals cell negative 7 end cell row x equals cell fraction numerator negative 7 over denominator 4 end fraction end cell row x equals cell negative 1 comma 75 end cell end table$

Oleh karena itu, jawaban yang benar adalah C. space