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For what value of x does (−6)^x = 6^(9−x)?

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For what value of x does (−6)^x = 6^(9−x)?  [#permalink]

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New post 01 Mar 2017, 02:02
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:34) correct 34% (01:28) wrong based on 155 sessions

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Re: For what value of x does (−6)^x = 6^(9−x)?  [#permalink]

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New post 01 Mar 2017, 09:58
1
2
Bunuel wrote:
For what value of x does \((−6)^x = 6^{(9−x)}\)?

A. −9/2
B. 0
C. 1
D. 9/2
E. There is no real-number solution


Hi

\(a^b = (-a)^b\) only if b is even.

In our case, expression to the right is always positive. In order for the expresion to the left to be positive x should be even, but 9-x when x is even will always be odd.
On the other hand, 9/2 or -9/2 will bring us square root of a negative number - complex number.

Answer E.
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Re: For what value of x does (−6)^x = 6^(9−x)?  [#permalink]

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New post 01 Mar 2017, 10:18
Answer is E, with options A,B,C the exponent part will never be equal on LHS and RHS....for option D the base on both sides are is equal only in mod, hence no real solution exists for the equation


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For what value of x does (−6)^x = 6^(9−x)?  [#permalink]

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New post 14 Feb 2019, 20:51
Bunuel wrote:
For what value of x does \((−6)^x = 6^{(9−x)}\)?

A. −9/2
B. 0
C. 1
D. 9/2
E. There is no real-number solution


Hello there math experts!!!

What's wrong with doing it like:

\((−6)^x = 6^{(9−x)}\) ... Let x be 9/2

\((−6)^-(9/2) = 6^{(9−(9/2))}\) is it possible to cancel out the minus from -6????

\((6)^(9/2) = 6^{((18-9)/2))}\)

\((6)^(9/2) = 6^{(9/2)}\)
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Re: For what value of x does (−6)^x = 6^(9−x)?  [#permalink]

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New post 18 Feb 2019, 19:13
Bunuel wrote:
For what value of x does \((−6)^x = 6^{(9−x)}\)?

A. −9/2
B. 0
C. 1
D. 9/2
E. There is no real-number solution


In order for the equation to be true, the exponents must be equal and they must be an even number such as 2 (notice that (-6)^2 = 6^2) or a fraction in lowest terms in the form of m/n where m is even and n is odd such as ⅔ (notice that (-6)^(⅔) = 6^(⅔)). However, setting the exponents equal, we find that:

x = 9 - x

2x = 9

x = 9/2

Since 9/2 is neither of the two cases mentioned above, there is no real-number solution that will allow -6^x to equal 6^(9-x).

Answer: E
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Re: For what value of x does (−6)^x = 6^(9−x)?   [#permalink] 18 Feb 2019, 19:13
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