Pertanyaan

Jika x > 0 dan x ≠ 1 memenuhi x 4 x 3 x = x p dengan p adalah bilangan rasional, maka p = ....

Jika x > 0 dan x ≠ 1 memenuhi $\frac{4 x 3 x}{x} = x^{p}$ dengan p adalah bilangan rasional, maka p = ....

M. Robo

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Ingat bahwa dan begin mathsize 14px style x to the power of b over x to the power of c equals x to the power of b minus c end exponent end style . Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator fourth root of x cube root of x end root over denominator x end fraction end cell equals cell x to the power of p end cell row cell fraction numerator fourth root of x times x to the power of 1 third end exponent end root over denominator x end fraction end cell equals cell x to the power of p end cell row cell fraction numerator fourth root of x to the power of 1 plus 1 third end exponent end root over denominator x end fraction end cell equals cell x to the power of p end cell row cell fraction numerator fourth root of x to the power of 4 over 3 end exponent end root over denominator x end fraction end cell equals cell x to the power of p end cell row cell x to the power of fraction numerator 4 over 3 over denominator 4 end fraction end exponent over x end cell equals cell x to the power of p end cell row cell x to the power of 4 over 3 times 1 fourth end exponent over x end cell equals cell x to the power of p end cell row cell x to the power of 1 third end exponent over x end cell equals cell x to the power of p end cell row cell x to the power of 1 third minus 1 end exponent end cell equals cell x to the power of p end cell row cell x to the power of negative 2 over 3 end exponent end cell equals cell x to the power of p end cell row blank blank blank end table end style$

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