Roboguru

Jika , nilai  adalah ....

Pertanyaan

Jika open parentheses 1 fourth close parentheses to the power of x plus 2 end exponent equals cube root of 8 to the power of 2 x minus 1 end exponent end root, nilai 81 to the power of x adalah ....

  1. 27 

  2. 9 

  3. 3 

  4. 1 over 9 

  5. 1 over 27 

Pembahasan Soal:

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.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Juli 2021

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