Pertanyaan

Jika 2 − 2 1 + 2 − 3 1 2 2 1 + 2 3 1 = 4 x , maka x = ...

Jika $\frac{2 ^{\frac{1}{2}} + 2 ^{\frac{1}{3}}}{2 ^{- \frac{1}{2}} + 2 ^{- \frac{1}{3}}} = 4^{x}$ , maka $x = ...$

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Jawaban terverifikasi

Jawaban

nilai adalah .

nilai

adalah

Pembahasan

Dengan menggunakan sifat bilangan berpangkat/eksponen: 1. 2. 3. 4. maka, Jadi, nilai adalah .

Dengan menggunakan sifat bilangan berpangkat/eksponen:

1. a to the power of negative n end exponent equals 1 over a to the power of n

2. a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent

3. left parenthesis a to the power of m right parenthesis to the power of n equals a to the power of m cross times n end exponent

4. a to the power of p equals a to the power of q left right double arrow p equals q

maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 to the power of begin display style 1 half end style end exponent plus 2 to the power of begin display style 1 third end style end exponent over denominator 2 to the power of negative begin display style 1 half end style end exponent plus 2 to the power of negative begin display style 1 third end style end exponent end fraction end cell equals cell 4 to the power of x end cell row cell fraction numerator 2 to the power of 1 half end exponent plus 2 to the power of 1 third end exponent over denominator begin display style 1 over 2 to the power of begin display style 1 half end style end exponent end style plus begin display style 1 over 2 to the power of 1 third end exponent end style end fraction end cell equals cell 4 to the power of x end cell row cell fraction numerator 2 to the power of 1 half end exponent plus 2 to the power of 1 third end exponent over denominator open parentheses begin display style fraction numerator 2 to the power of 1 third end exponent plus 2 to the power of 1 half end exponent over denominator 2 to the power of begin display style 1 half end style end exponent cross times 2 to the power of begin display style 1 third end style end exponent end fraction end style close parentheses end fraction end cell equals cell 4 to the power of x end cell row cell up diagonal strike open parentheses 2 to the power of 1 half end exponent plus 2 to the power of 1 third end exponent close parentheses end strike cross times fraction numerator open parentheses 2 to the power of begin display style 1 half end style end exponent cross times 2 to the power of begin display style 1 third end style end exponent close parentheses over denominator up diagonal strike open parentheses 2 to the power of 1 third end exponent plus 2 to the power of 1 half end exponent close parentheses end strike end fraction end cell equals cell 4 to the power of x end cell row cell 2 to the power of 1 half plus 1 third end exponent end cell equals cell 4 to the power of x end cell row cell 2 to the power of 5 over 6 end exponent end cell equals cell 2 to the power of 2 x end exponent end cell row cell 5 over 6 end cell equals cell 2 x end cell row cell 5 over 12 end cell equals x row x equals cell 5 over 12 end cell end table end style$

Jadi, nilai adalah 5 over 12 .