Explanation

First, rewrite 0.02 as a fraction, \(\frac{2}{100}\). For \(\frac{2}{3^x}\) to be less than \(\frac{2}{100}\) \(3^x\) must be greater than 100.

Plugging In the Answers is the easiest way to get this right. Choice (E) is \(3^4\) = 81 and the fraction is greater than 0.02; eliminate it.

Choice (D) is \(3^5\) = 243 and this makes the fraction inequality would be true if the denominator of less than 0.02. Therefore, the least value for x is 5. Be sure to answer what is asked. The \(\frac{2}{3^x}\) were 101, which is choice (B); however, the question is asking for the least value of x, not of 3x, so the correct answer is choice D.

The correct option is D.
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3^X OR X^3 ? I am confused

Your question is not clear. What do you mean by \(3^X\) OR \(X^3\)
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