Nilai x yang memenuhi persamaan 223x−1=481−3xadalah ....

Pertanyaan

Nilai $x$ yang memenuhi persamaan $2\sqrt{2^{3x-1}}=4\sqrt{8^{1-3x}}$ adalah ....

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B. space

Pembahasan

Ingat kembali:

Jika dan maka
dengan

Oleh karena persamaan dapat diubah menjadi bentuk seperti berikut:

$2 square root of 2 to the power of 3 x minus 1 end exponent end root equals 4 square root of 8 to the power of 1 minus 3 x end exponent end root 2 to the power of 1 square root of 2 to the power of 3 x minus 1 end exponent end root equals 2 squared square root of open parentheses 2 cubed close parentheses to the power of 1 minus 3 x end exponent end root 2 to the power of 1 square root of 2 to the power of 3 x minus 1 end exponent end root equals 2 squared square root of 2 to the power of 3 minus 9 x end exponent end root 2 to the power of 1 times 2 to the power of fraction numerator 3 x minus 1 over denominator 2 end fraction end exponent equals 2 squared times 2 to the power of fraction numerator 3 minus 9 x over denominator 2 end fraction end exponent 2 to the power of 1 plus fraction numerator 3 x minus 1 over denominator 2 end fraction end exponent equals 2 to the power of 2 plus fraction numerator 3 minus 9 x over denominator 2 end fraction end exponent 2 to the power of 2 over 2 plus fraction numerator 3 x minus 1 over denominator 2 end fraction end exponent equals 2 to the power of 4 over 2 plus fraction numerator 3 minus 9 x over denominator 2 end fraction end exponent 2 to the power of fraction numerator 3 x minus 1 plus 2 over denominator 2 end fraction end exponent equals 2 to the power of fraction numerator 4 plus 3 minus 9 x over denominator 2 end fraction end exponent 2 to the power of fraction numerator 3 x plus 1 over denominator 2 end fraction end exponent equals 2 to the power of fraction numerator 7 minus 9 x over denominator 2 end fraction end exponent$

maka diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 x plus 1 over denominator 2 end fraction end cell equals cell fraction numerator 7 minus 9 x over denominator 2 end fraction end cell row cell 3 x plus 1 end cell equals cell 7 minus 9 x end cell row cell 3 x end cell equals cell 7 minus 9 x minus 1 end cell row cell 3 x plus 9 x end cell equals cell 7 minus 1 end cell row cell 12 x end cell equals 6 row x equals cell 6 over 12 end cell row x equals cell fraction numerator 6 divided by 6 over denominator 12 divided by 6 end fraction end cell row x equals cell 1 half end cell end table$

Oleh karena itu, jawaban yang benar adalah B. space