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# The expression (x - a)^a/a^(x - a) = 1 is true for which of the

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Math Expert
Joined: 02 Sep 2009
Posts: 47110
The expression (x - a)^a/a^(x - a) = 1 is true for which of the [#permalink]

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10 Sep 2017, 05:07
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Difficulty:

45% (medium)

Question Stats:

67% (00:56) correct 33% (00:45) wrong based on 42 sessions

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The expression $$\frac{(x - a)^a}{a^{(x - a)}}=1$$ is true for which of the following values for x and a?

A. x = 1 and a = 0
B. x = 0 and a = 1
C. x = 1 and a = 1
D. x = 2 and a = 1
E. x = 1 and a = 2

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Re: The expression (x - a)^a/a^(x - a) = 1 is true for which of the [#permalink]

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10 Sep 2017, 12:36
Bunuel wrote:
The expression $$\frac{(x - a)^a}{a^{(x - a)}}=1$$ is true for which of the following values for x and a?

A. x = 1 and a = 0
B. x = 0 and a = 1
C. x = 1 and a = 1
D. x = 2 and a = 1
E. x = 1 and a = 2

As per the question $$(x-a)^a = a^{x-a}$$. In an equation this can only be true when Base of RHS = Base of LHS and Exponent of RHS = Exponent of LHS
this implies $$x-a = a$$ or $$x = 2a$$

Only Option D satisfies the relation between $$x$$ & $$a$$

We can also substitute the values of $$x$$ & $$a$$ from the options to test the equation

Option $$D$$
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Joined: 07 Dec 2016
Posts: 41
Re: The expression (x - a)^a/a^(x - a) = 1 is true for which of the [#permalink]

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11 Sep 2017, 13:25
Option D

Substituted the values given in options and checked the equality
Re: The expression (x - a)^a/a^(x - a) = 1 is true for which of the   [#permalink] 11 Sep 2017, 13:25
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