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If 5^x = 5^(3x), what is the value of x?

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If 5^x = 5^(3x), what is the value of x? [#permalink]

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New post 06 Jan 2017, 03:05
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A
B
C
D
E

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  15% (low)

Question Stats:

74% (00:33) correct 26% (00:16) wrong based on 74 sessions

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Re: If 5^x = 5^(3x), what is the value of x? [#permalink]

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New post 06 Jan 2017, 03:16
Bunuel wrote:
If 5^x = 5^(3x), what is the value of x?

A. –1
B. 0
C. 1
D. 3
E. It cannot be determined from the information given.



Though 5^x = 5^(3x) can not be solved algebraically, the equality holds true when x = 0 in which case 1 = 1.
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Re: If 5^x = 5^(3x), what is the value of x? [#permalink]

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New post 06 Jan 2017, 07:53
Bases are equal, so exponents must be equal
3x=x => x=0

B.

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Re: If 5^x = 5^(3x), what is the value of x? [#permalink]

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New post 06 Jan 2017, 08:23
Bunuel wrote:
If 5^x = 5^(3x), what is the value of x?

A. –1
B. 0
C. 1
D. 3
E. It cannot be determined from the information given.


\(5^x = 5^{3x}\)

So, \(x = 3x\)

Thus, the only possible answer to the above is only when x = 0

Hence, answer will be (B) 0

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Re: If 5^x = 5^(3x), what is the value of x? [#permalink]

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New post 07 Jan 2017, 03:31
ANS B
PUTTING THE VALUES IN THE EQUATION AND FINDING THE ANSWER.
5^X=5^3X X=0 1=1
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Re: If 5^x = 5^(3x), what is the value of x? [#permalink]

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New post 09 Jan 2017, 10:36
Bunuel wrote:
If 5^x = 5^(3x), what is the value of x?

A. –1
B. 0
C. 1
D. 3
E. It cannot be determined from the information given.


Recall that if a^m = a^n, and a is not equal to -1, 0, or 1, then m = n. In other words, if the bases are equal (as long as the base is not -1, 0, or 1), then the exponents are equal. Thus, we can drop the base 5 and set x = 3x. The only value that satisfies the equation is x = 0.

Answer: B
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Re: If 5^x = 5^(3x), what is the value of x? [#permalink]

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New post 11 Apr 2017, 01:16
If 5^x = 5^(3x), then x = 3x so 2x=0 => x=0 Ans. B
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Re: If 5^x = 5^(3x), what is the value of x?   [#permalink] 11 Apr 2017, 01:16
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