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06 Dec 2015, 11:55
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C
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If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?
A. 5
B. 4
C. 3
D. 2
E. 1
A. 5
B. 4
C. 3
D. 2
E. 1
Updated on: 28 May 2020, 09:24
Originally posted by BrentGMATPrepNow on 29 Oct 2016, 09:48.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:24, edited 2 times in total.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:24, edited 2 times in total.
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Bunuel
If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?
A. 5
B. 4
C. 3
D. 2
E. 1
The important concept here is: (negative number)^(even integer) = some positive valueA. 5
B. 4
C. 3
D. 2
E. 1
Examples
(-5)^2 = 25
(-3)^4 = 81
(-1)^10 = 1
(-2)^6 = 64
Also notice that:
(-5)^2 = (5)^2 = 25
(-3)^4 = (3)^4 = 81
(-1)^10 = (1)^10 = 1
(-2)^6 = (2)^6 = 64
The same can be said for ANY negative value raised to an EVEN power
Now onto the question.............
Since 4x is EVEN for any integer x, we can write:
(-5)^(4x) = (5)^(4x)
So, we can write: 5^(4x) = 5^(9 + x)
Since we now have the base, we can conclude that 4x = 9 + x
Solve to get: x = 3
Answer: C
General Discussion
06 Dec 2015, 20:27
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Since x is an integer, (-5)^4x is always positive.
So, 5^4x = 5^(9 + x)
4x = 9 + x
3x = 9
x = 3
Answer: C
So, 5^4x = 5^(9 + x)
4x = 9 + x
3x = 9
x = 3
Answer: C
