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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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06 Jan 2017, 02:05
00:00

Difficulty:

5% (low)

Question Stats:

78% (00:38) correct 22% (00:26) wrong based on 99 sessions

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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.

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

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06 Jan 2017, 02:16
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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06 Jan 2017, 06:53
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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06 Jan 2017, 07:23
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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07 Jan 2017, 02:31
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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09 Jan 2017, 09:36
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.

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

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11 Apr 2017, 00:16
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]

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30 Jun 2018, 19:38
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Re: If 5^x = 5^(3x), what is the value of x? &nbs [#permalink] 30 Jun 2018, 19:38
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