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For how many integers x is 3^x = x^3 ?

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Bunuel
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For how many integers x is 3^x = x^3 ? [#permalink] New post   19 Oct 2021, 03:45
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For how many integers x is \(3^x = x^3\) ?

(A) None
(B) One
(C) Two
(D) Three
(E) More than three
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B
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stne
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For how many integers x is 3^x = x^3 ? [#permalink] New post   Updated on: 31 Oct 2021, 04:35
Bunuel wrote:
For how many integers x is \(3^x = x^3\) ?

(A) None
(B) One
(C) Two
(D) Three
(E) More than three



Not sure if there is any alzebraic method to solve this, if there is please do share.

Method used here is testing various numbers

Tried with a couple of numbers and found that only \(3\) satisfies.

Hence only one value

Ans B

Hope it helps.

Originally posted by stne on 30 Oct 2021, 19:51.
Last edited by stne on 31 Oct 2021, 04:35, edited 1 time in total.
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Re: For how many integers x is 3^x = x^3 ? [#permalink] New post   30 Oct 2021, 19:59
Bunuel wrote:
For how many integers x is \(3^x = x^3\) ?

(A) None
(B) One
(C) Two
(D) Three
(E) More than three


Since x is an integer, it can’t be negative otherwise 3*x will be a fraction and x^3 will be an integer. x can’t be 0 too. Only possible value is 3. For any integer x>3 , 3^x will be greater than x^3

Answer is 1, option B

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Rahul257
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Re: For how many integers x is 3^x = x^3 ? [#permalink] New post   30 Oct 2021, 20:10
Knowing the graphs of a^x and x^3 will help. The two graphs intersect only at one point and hence only one solution to the equation.

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Re: For how many integers x is 3^x = x^3 ? [#permalink]
30 Oct 2021, 20:10
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