Pertanyaan

Hitunglah nilai x yang memenuhi persamaan 5 2 x − 3 2 x = 5 2 x − 1 + 3 2 x − 1 .

Hitunglah nilai $x$ yang memenuhi persamaan $5^{2 x} - 3^{2 x} = 5^{2 x - 1} + 3^{2 x - 1}$ .

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai yang memenuhi persamaan tersebut adalah .

nilai

yang memenuhi persamaan tersebut adalah 1 half

Pembahasan

Ingat kembali bentuk persamaan eksponen berikut: Persamaan , dapat diubah menjadi: Sehingga: Jadi, nilai yang memenuhi persamaan tersebut adalah .

Ingat kembali bentuk persamaan eksponen berikut:

Persamaan 5 to the power of 2 x end exponent minus 3 to the power of 2 x end exponent equals 5 to the power of 2 x minus 1 end exponent plus 3 to the power of 2 x minus 1 end exponent , dapat diubah menjadi:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 5 to the power of 2 x end exponent minus 3 to the power of 2 x end exponent end cell equals cell 5 to the power of 2 x minus 1 end exponent plus 3 to the power of 2 x minus 1 end exponent end cell row cell 5 to the power of 2 x end exponent minus 3 to the power of 2 x end exponent end cell equals cell 5 to the power of 2 x end exponent times 5 to the power of negative 1 end exponent plus 3 to the power of 2 x end exponent times 3 to the power of negative 1 end exponent end cell row cell 5 to the power of 2 x end exponent minus 3 to the power of 2 x end exponent end cell equals cell 5 to the power of 2 x end exponent times 1 fifth plus 3 to the power of 2 x end exponent times 1 third end cell row cell 5 to the power of 2 x end exponent minus 3 to the power of 2 x end exponent end cell equals cell 5 to the power of 2 x end exponent over 5 plus 3 to the power of 2 x end exponent over 3 end cell row cell 5 to the power of 2 x end exponent minus 5 to the power of 2 x end exponent over 5 end cell equals cell 3 to the power of 2 x end exponent over 3 plus 3 to the power of 2 x end exponent end cell row cell 5 to the power of 2 x end exponent open parentheses 1 minus 1 fifth close parentheses end cell equals cell 3 to the power of 2 x end exponent open parentheses 1 third plus 1 close parentheses end cell row cell 5 to the power of 2 x end exponent open parentheses 5 over 5 minus 1 fifth close parentheses end cell equals cell 3 to the power of 2 x end exponent open parentheses 1 third plus 3 over 3 close parentheses end cell row cell 5 to the power of 2 x end exponent open parentheses fraction numerator up diagonal strike 4 over denominator 5 end fraction close parentheses end cell equals cell 3 to the power of 2 x end exponent open parentheses fraction numerator up diagonal strike 4 over denominator 3 end fraction close parentheses end cell row cell 5 to the power of 2 x end exponent open parentheses 1 fifth close parentheses end cell equals cell 3 to the power of 2 x end exponent open parentheses 1 third close parentheses end cell row cell 5 to the power of 2 x end exponent open parentheses 5 to the power of negative 1 end exponent close parentheses end cell equals cell 3 to the power of 2 x end exponent open parentheses 3 to the power of negative 1 end exponent close parentheses end cell row cell 5 to the power of 2 x minus 1 end exponent end cell equals cell 3 to the power of 2 x minus 1 end exponent end cell end table$

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 1 end cell equals 0 row cell 2 x end cell equals 1 row x equals cell 1 half end cell end table

Jadi, nilai yang memenuhi persamaan tersebut adalah 1 half .