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

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VP
Joined: 12 Feb 2015
Posts: 1010
For how many integers x is 3^x = x^3 ?  [#permalink]

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07 Dec 2019, 03:41
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00:00

Difficulty:

35% (medium)

Question Stats:

64% (01:14) correct 36% (01:01) wrong based on 41 sessions

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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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Manish

"Only I can change my life. No one can do it for me"
Senior Manager
Joined: 28 Feb 2014
Posts: 277
Location: India
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
Re: For how many integers x is 3^x = x^3 ?  [#permalink]

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07 Dec 2019, 05:15
CAMANISHPARMAR wrote:
For how many integers $$x$$ is $$3^x$$ = $$x^3$$?

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

only possible case x=3

IMO B
Intern
Joined: 12 Oct 2019
Posts: 9
Re: For how many integers x is 3^x = x^3 ?  [#permalink]

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08 Dec 2019, 00:24
2 cases are possible
0 and 3

Posted from my mobile device
VP
Joined: 12 Feb 2015
Posts: 1010
Re: For how many integers x is 3^x = x^3 ?  [#permalink]

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08 Dec 2019, 02:39
Psyllium9 wrote:
2 cases are possible
0 and 3

Posted from my mobile device

If $$x$$ = 0 then after substituting for x we get on the L.H.S "one" (i.e. for $$3^x$$) which is not equal to "zero" (i.e. for $$x^3$$)

Hence $$x$$ = 0 is not possible
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Manish

"Only I can change my life. No one can do it for me"
Re: For how many integers x is 3^x = x^3 ?   [#permalink] 08 Dec 2019, 02:39
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