4291. $$ (\sqrt[3]{2})^{x-1}=\left(\frac{2}{\sqrt[3]{2}} ight)^{2 x} $$ tenglamani yeching. $$ \begin{array}{llll} ext { A) }-\frac{1}{5} & ext { B) } \frac{1}{3} & ext { C) }-\frac{1}{3} & ext { D) }-\frac{1}{4}\end{array} $$

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4291. $$ (\sqrt[3]{2})^{x-1}=\left(\frac{2}{\sqrt[3]{2}}ight)^{2 x} $$ tenglamani yeching. $$ \begin{array}{llll}	ext { A) }-\frac{1}{5} & 	ext { B) } \frac{1}{3} & 	ext { C) }-\frac{1}{3} & 	ext { D) }-\frac{1}{4}\end{array} $$

UpStudy AI · Accepted Answer

Solve the equation $$ (\sqrt[3]{2})^{x-1}=\left(\frac{2}{\sqrt[3]{2}}\right)^{2x} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\left(\sqrt[3]{2}\right)^{x-1}=\left(\frac{2}{\sqrt[3]{2}}\right)^{2x}$$
- step1: Rewrite the expression:
  $$2^{\frac{1}{3}x-\frac{1}{3}}=2^{\frac{4}{3}x}$$
- step2: Set the exponents equal:
  $$\frac{1}{3}x-\frac{1}{3}=\frac{4}{3}x$$
- step3: Move the variable to the left side:
  $$\frac{1}{3}x-\frac{1}{3}-\frac{4}{3}x=0$$
- step4: Subtract the terms:
  $$-x-\frac{1}{3}=0$$
- step5: Move the constant to the right side:
  $$-x=0+\frac{1}{3}$$
- step6: Remove 0:
  $$-x=\frac{1}{3}$$
- step7: Change the signs:
  $$x=-\frac{1}{3}$$
The solution to the equation $$ (\sqrt[3]{2})^{x-1}=\left(\frac{2}{\sqrt[3]{2}}\right)^{2x} $$ is $$ x=-\frac{1}{3} $$ or $$ x=-0.\dot{3} $$.

Therefore, the correct answer is C) $$-\frac{1}{3}$$.
$$ x=-\frac{1}{3} $$. Therefore, the correct answer is C) $$-\frac{1}{3}$$.

tenglamani yeching.

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