Pertanyaan

Jika 4 x 3 ⋅ x 5 ⋅ 3 x = 3 x 2 c ⋅ x 3 c ⋅ 4 x c dengan x > 0 dan x  = 1 , maka nilai yang memenuhi adalah....

Jika $4 x^{3} \cdot x^{5} \cdot 3 x = 3 x^{2 c} \cdot x^{3 c} \cdot 4 x^{c}$ dengan $x > 0$ dan $x \neq = 1,$ maka nilai $c$ yang memenuhi adalah ....

R. Tri

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan perhitungan berikut! Jadi, jawaban yang tepat adalah D.

Perhatikan perhitungan berikut!

$table attributes columnalign right center left columnspacing 0px end attributes row cell fourth root of x cubed times square root of x to the power of 5 times cube root of x end root end root end cell equals cell cube root of x to the power of 2 c end exponent times square root of x to the power of 3 c end exponent times fourth root of x to the power of c end root end root end root end cell row cell fourth root of x cubed times square root of x to the power of 5 times x to the power of 1 third end exponent end root end root end cell equals cell cube root of x to the power of 2 c end exponent times square root of x to the power of 3 c end exponent times x to the power of c over 4 end exponent end root end root end cell row cell fourth root of x cubed times square root of x to the power of 5 plus 1 third end exponent end root end root end cell equals cell cube root of x to the power of 2 c end exponent times square root of x to the power of 3 c plus c over 4 end exponent end root end root end cell row cell fourth root of x cubed times square root of x to the power of 16 over 3 end exponent end root end root end cell equals cell cube root of x to the power of 2 c end exponent times square root of x to the power of fraction numerator 13 c over denominator 4 end fraction end exponent end root end root end cell row cell fourth root of x cubed times x to the power of fraction numerator 16 over 3 over denominator 2 end fraction end exponent end root end cell equals cell cube root of x to the power of 2 c end exponent times x to the power of fraction numerator fraction numerator 13 c over denominator 4 end fraction over denominator 2 end fraction end exponent end root end cell row cell fourth root of x cubed times x to the power of 16 over 3 times 1 half end exponent end root end cell equals cell cube root of x to the power of 2 c end exponent times x to the power of fraction numerator 13 c over denominator 4 end fraction times 1 half end exponent end root end cell row cell fourth root of x cubed times x to the power of 8 over 3 end exponent end root end cell equals cell cube root of x to the power of 2 c end exponent times x to the power of fraction numerator 13 c over denominator 8 end fraction end exponent end root end cell row cell fourth root of x to the power of 3 plus 8 over 3 end exponent end root end cell equals cell cube root of x to the power of 2 c plus fraction numerator 13 c over denominator 8 end fraction end exponent end root end cell row cell fourth root of x to the power of 17 over 3 end exponent end root end cell equals cell cube root of x to the power of fraction numerator 29 c over denominator 8 end fraction end exponent end root end cell row cell x to the power of fraction numerator 17 over 3 over denominator 4 end fraction end exponent end cell equals cell x to the power of fraction numerator fraction numerator 29 c over denominator 8 end fraction over denominator 3 end fraction end exponent end cell row cell x to the power of 17 over 3 times 1 fourth end exponent end cell equals cell x to the power of fraction numerator 29 c over denominator 8 end fraction times 1 third end exponent end cell row cell x to the power of 17 over 12 end exponent end cell equals cell x to the power of fraction numerator 29 c over denominator 24 end fraction end exponent end cell row cell 17 over 12 end cell equals cell fraction numerator 29 c over denominator 24 end fraction end cell row cell 17 over 12 times 24 over 29 end cell equals cell fraction numerator 29 c over denominator 24 end fraction times 24 over 29 end cell row cell 17 over up diagonal strike 12 to the power of 1 times up diagonal strike 24 squared over 29 end cell equals cell fraction numerator down diagonal strike 29 c over denominator horizontal strike 24 end fraction times fraction numerator horizontal strike 24 over denominator down diagonal strike 29 end fraction end cell row cell 34 over 29 end cell equals c end table$

Jadi, jawaban yang tepat adalah D.