Pertanyaan

Jika ( 4 1 ) x + 2 = 3 8 2 x − 1 , nilai 8 1 x adalah ....

Jika $(\frac{1}{4})^{x + 2} = 3 8^{2 x - 1}$ , nilai $8 1^{x}$ adalah ....

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Ingat kembali bentuk persamaan eksponen berikut: Maka: Sehingga: Jadi, jawaban yang benar adalah E.

Ingat kembali bentuk persamaan eksponen berikut:

straight a to the power of straight f open parentheses straight x close parentheses end exponent equals straight a to the power of straight m comma space straight a greater than 0 space rightwards arrow space straight f open parentheses straight x close parentheses equals straight m

Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 1 fourth close parentheses to the power of x plus 2 end exponent end cell equals cell cube root of 8 to the power of 2 x minus 1 end exponent end root end cell row cell open parentheses 1 over 2 squared close parentheses to the power of x plus 2 end exponent end cell equals cell cube root of open parentheses 2 cubed close parentheses to the power of 2 x minus 1 end exponent end root end cell row cell open parentheses 2 to the power of negative 2 end exponent close parentheses to the power of x plus 2 end exponent end cell equals cell cube root of 2 to the power of 3 open parentheses 2 x minus 1 close parentheses end exponent end root end cell row cell 2 to the power of negative 2 x minus 4 end exponent end cell equals cell 2 to the power of fraction numerator up diagonal strike 3 open parentheses 2 x minus 1 close parentheses over denominator up diagonal strike 3 end fraction end exponent end cell row cell 2 to the power of negative 2 x minus 4 end exponent end cell equals cell 2 to the power of 2 x minus 1 end exponent end cell row cell negative 2 x minus 4 end cell equals cell 2 x minus 1 end cell row cell negative 2 x minus 2 x end cell equals cell negative 1 plus 4 end cell row cell negative 4 x end cell equals 3 row x equals cell negative 3 over 4 end cell end table$

Sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 81 to the power of x end cell equals cell 81 to the power of negative 3 over 4 end exponent end cell row blank equals cell open parentheses 3 to the power of up diagonal strike 4 end exponent close parentheses to the power of negative fraction numerator 3 over denominator up diagonal strike 4 end fraction end exponent end cell row blank equals cell 3 to the power of negative 3 end exponent end cell row blank equals cell 1 over 3 cubed end cell row blank equals cell 1 over 27 end cell end table$

Jadi, jawaban yang benar adalah E.