Pertanyaan

Penyelesaian dari persamaan 25 5 3 x ⋅ 12 5 3 x = 5 2 x 12 5 x − 2 adalah ....

Penyelesaian dari persamaan $25 5^{3 x} \cdot 12 5^{3 x} = \frac{12 5 ^{x - 2}}{5 ^{2 x}}$ adalah ....

I. Ridha

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

jawaban yang benar adalah B. space

Pembahasan

Ingat kembali: Jika dengan dan a  = 1 , maka dengan dengan Dengan demikian, sehingga karena a = 5 yang berarti dan a  = 1 , maka diperoleh Oleh karena itu, jawaban yang benar adalah B.

Ingat kembali:

Jika dengan dan $a \neq = 1$ , maka
dengan
dengan

Dengan demikian,

$table attributes columnalign right center left columnspacing 0px end attributes row cell 25 square root of 5 to the power of 3 x end exponent end root times square root of 125 to the power of 3 x end exponent end root end cell equals cell 125 to the power of x minus 2 end exponent over 5 to the power of 2 x end exponent end cell row cell 5 squared times square root of 5 to the power of 3 x end exponent end root times square root of open parentheses 5 cubed close parentheses to the power of 3 x end exponent end root end cell equals cell open parentheses 5 cubed close parentheses to the power of x minus 2 end exponent times 5 to the power of negative 2 x end exponent end cell row cell 5 squared times square root of 5 to the power of 3 x end exponent end root times square root of 5 to the power of 9 x end exponent end root end cell equals cell 5 to the power of 3 x minus 6 end exponent times 5 to the power of negative 2 x end exponent end cell row cell 5 squared times 5 to the power of fraction numerator 3 x over denominator 2 end fraction end exponent times 5 to the power of fraction numerator 9 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of 3 x minus 6 end exponent times 5 to the power of negative 2 x end exponent end cell row cell 5 to the power of 2 plus fraction numerator 3 x over denominator 2 end fraction plus fraction numerator 9 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of 3 x minus 6 plus open parentheses negative 2 x close parentheses end exponent end cell row cell 5 to the power of 4 over 2 plus fraction numerator 3 x over denominator 2 end fraction plus fraction numerator 9 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of 3 x minus 6 plus open parentheses negative 2 x close parentheses end exponent end cell row cell 5 to the power of fraction numerator 4 plus 3 x plus 9 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of 3 x minus 6 plus open parentheses negative 2 x close parentheses end exponent end cell row cell 5 to the power of fraction numerator 4 plus 12 x over denominator 2 end fraction end exponent end cell equals cell 5 to the power of x minus 6 end exponent end cell end table$

sehingga karena $a = 5$ yang berarti a greater than 0 dan $a \neq = 1$ , maka diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 4 plus 12 x over denominator 2 end fraction end cell equals cell x minus 6 end cell row cell 4 plus 12 x end cell equals cell open parentheses x minus 6 close parentheses cross times 2 end cell row cell 4 plus 12 x end cell equals cell 2 x minus 12 end cell row cell 12 x end cell equals cell 2 x minus 12 minus 4 end cell row cell 12 x minus 2 x end cell equals cell negative 12 minus 4 end cell row cell 10 x end cell equals cell negative 16 end cell row x equals cell fraction numerator negative 16 over denominator 10 end fraction end cell row x equals cell negative 1 comma 6 end cell end table$

Oleh karena itu, jawaban yang benar adalah B. space