Pertanyaan

Nilai x yang memenuhi persamaan 3 2 7 3 3 x − 5 = 9 8 1 2 x − 2 3 adalah ....

Nilai x yang memenuhi persamaan $3 2 7^{\frac{3 x}{3} - 5} = 9 8 1^{2 x - \frac{3}{2}}$ adalah ....

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N. Rahayu

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Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa Dengan demikian, nilai x yang memenuhi persamaan tersebut adalah . Jadi, jawaban yang tepat adalah A.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of 27 to the power of fraction numerator 3 x over denominator 3 end fraction minus 5 end exponent end root end cell equals cell 9 square root of 81 to the power of 2 x minus 3 over 2 end exponent end root end cell row cell cube root of left parenthesis 3 cubed right parenthesis to the power of fraction numerator 3 x over denominator 3 end fraction minus 5 end exponent end root end cell equals cell 3 squared square root of left parenthesis 3 to the power of 4 right parenthesis to the power of 2 x minus 3 over 2 end exponent end root end cell row cell cube root of 3 to the power of 3 x minus 15 end exponent end root end cell equals cell 3 squared square root of 3 to the power of 8 x minus 6 end exponent end root end cell row cell left parenthesis 3 to the power of 3 x minus 15 end exponent right parenthesis to the power of 1 third end exponent end cell equals cell 3 squared cross times left parenthesis 3 to the power of 8 x minus 6 end exponent right parenthesis to the power of 1 half end exponent end cell row cell 3 to the power of 3 x times 1 third minus 15 times 1 third end exponent end cell equals cell 3 squared cross times 3 to the power of 8 x times 1 half minus 6 times 1 half end exponent end cell row cell 3 to the power of x minus 5 end exponent end cell equals cell 3 squared cross times 3 to the power of 4 x minus 3 end exponent end cell row cell 3 to the power of x minus 5 end exponent end cell equals cell 3 to the power of 2 plus 4 x minus 3 end exponent end cell row cell 3 to the power of x minus 5 end exponent end cell equals cell 3 to the power of 4 x minus 1 end exponent end cell row cell x minus 5 end cell equals cell 4 x minus 1 end cell row cell x minus 4 x end cell equals cell negative 1 plus 5 end cell row cell negative 3 x end cell equals 4 row x equals cell negative 4 over 3 end cell end table end style$

Dengan demikian, nilai x yang memenuhi persamaan tersebut adalah .

Jadi, jawaban yang tepat adalah A.