Pertanyaan

Tentukan nilai x yang memenuhi pada: 5 x − 3 ( 5 − x ) 5 x + 5 − x = 3

Tentukan nilai $x$ yang memenuhi pada:

$\frac{5 ^{x} + 5 ^{- x}}{5 ^{x} - 3 ( 5 ^{- x} )} = 3$

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Jawaban terverifikasi

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nilai yang memenuhi persamaan di atas adalah .

nilai

yang memenuhi persamaan di atas adalah x equals 1 half

Pembahasan

Ingatlah sifat bilangan berpangkat sebagai berikut. Berdasarkan sifat di atas, maka: Dengan demikian, nilai yang memenuhi persamaan di atas adalah .

Ingatlah sifat bilangan berpangkat sebagai berikut.

a to the power of m a to the power of n equals a to the power of m plus n end exponent

Berdasarkan sifat di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 to the power of x plus 5 to the power of negative x end exponent over denominator 5 to the power of x minus 3 open parentheses 5 to the power of negative x end exponent close parentheses end fraction end cell equals 3 row cell fraction numerator 5 to the power of x plus 5 to the power of x minus 2 x end exponent over denominator 5 to the power of x minus 3 open parentheses 5 to the power of x minus 2 x end exponent close parentheses end fraction end cell equals 3 row cell fraction numerator 5 to the power of x plus 5 to the power of x times 5 to the power of negative 2 x end exponent over denominator 5 to the power of x minus 3 open parentheses 5 to the power of x times 5 to the power of negative 2 x end exponent close parentheses end fraction end cell equals 3 row cell fraction numerator 5 to the power of x plus 5 to the power of x times 5 to the power of negative 2 x end exponent over denominator 5 to the power of x minus 3 times 5 to the power of x times 5 to the power of negative 2 x end exponent end fraction end cell equals 3 row cell fraction numerator up diagonal strike 5 to the power of x end strike open parentheses 1 plus 5 to the power of negative 2 x end exponent close parentheses over denominator up diagonal strike 5 to the power of x end strike open parentheses 1 minus 3 times 5 to the power of negative 2 x end exponent close parentheses end fraction end cell equals 3 row cell fraction numerator 1 plus 5 to the power of negative 2 x end exponent over denominator 1 minus 3 times 5 to the power of negative 2 x end exponent end fraction end cell equals 3 row cell 1 plus 5 to the power of negative 2 x end exponent end cell equals cell 3 open parentheses 1 minus 3 times 5 to the power of negative 2 x end exponent close parentheses end cell row cell 1 plus 5 to the power of negative 2 x end exponent end cell equals cell 3 minus 9 times 5 to the power of negative 2 x end exponent end cell row cell 5 to the power of negative 2 x end exponent plus 9 times 5 to the power of negative 2 x end exponent end cell equals cell 3 minus 1 end cell row cell 10 times 5 to the power of negative 2 x end exponent end cell equals 2 row cell open parentheses 5 times 2 close parentheses times 5 to the power of negative 2 x end exponent end cell equals 2 row cell 5 times 5 to the power of negative 2 x end exponent end cell equals 1 row cell 5 to the power of 1 minus 2 x end exponent end cell equals cell 5 to the power of 0 end cell row cell 1 minus 2 x end cell equals 0 row cell 2 x end cell equals 1 row x equals cell 1 half end cell end table$

Dengan demikian, nilai yang memenuhi persamaan di atas adalah x equals 1 half .