Pertanyaan

Jika x > 0 dan x ≠ 1 memenuhi x 3 x x = x p , p bilangan rasional, maka p = ....

Jika x > 0 dan x ≠ 1 memenuhi $\frac{3 x x}{x} = x^{p}$ , p bilangan rasional, maka p = ....

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H. Nufus

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Pembahasan

$begin mathsize 14px style fraction numerator cube root of x square root of x end root over denominator x end fraction equals x to the power of p fraction numerator x to the power of begin display style 1 third end style end exponent x to the power of 1 over 6 end exponent over denominator x end fraction equals x to the power of p open parentheses x. x to the power of begin display style 1 half end style end exponent close parentheses to the power of begin display style 1 third end style end exponent over x equals x to the power of p open parentheses x to the power of begin display style 3 over 2 end style end exponent close parentheses to the power of begin display style 1 third end style end exponent over x equals x to the power of p x to the power of begin display style 1 half end style end exponent over x equals x to the power of p x to the power of negative 1 half end exponent equals x to the power of p p equals negative 1 half end style$