If 3^x>10, which of the following must be true?

The problem says given the premise that 3^x > 10, then x is... So x can't be 2.01 since 3^2.01 is not greater than 10. However, we know x is 2 point something. Now let's say that 2.1 is the smallest value such that 3^2.1 > 10. Thus, we cannot say that x must be greater than 3 (or 4), since 2.1, 2.2, 2.3, etc. are not greater than 3 (or 4), but it's true to say x must be greater than 2.

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As the question does not mention that x is an integer, x=2.01 then 3^2.01 = 9.09, which is not greater than 10. Hence x>10 cannot be the right answer.

Also, the question states that "which ones of these must be true". Any number with x>3 and x>4 will always be true, so why not select these options, as they supply the right numbers

habdo , I agree with you. I toggled between answers A and E. I picked A on a gamble. Nothing more.

MathRevolution , thank you for posting the question. It seems to me that by definition, if x > 2, it must also be greater than 3 and 4 unless there is an upper limit restriction, and here there is not.

I understand that Option I is the minimum condition which satisfies the inequality.

That is, x must be greater than 2 for \(3^{x}\) to be greater than 10.

But as I understand the word "must," in logic and in math, "must" includes the transitive cases:

If 3 > 2, and 2 > x, then 3 > x

I am not sure how one could argue that the third statement "must not" be true. Am I missing something?

=> 3^x > 10 > 3^2
Thus x > 2

Ans: A

I'm mixed up with this one.
Kudos if you agree!

ScottTargetTestPrep by the same logic then, \(x=2.01\) would be greater than 2, however \(3^x\) would not (as not given that \(x=integer\))

Same concept, why not II and III


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