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If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?
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21 Feb 2021, 10:50
21 Feb 2021, 10:50
Expert Reply
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Question Stats:
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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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 5
B. 4
C. 3
D. 2
E. 1
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?
[#permalink]
21 Feb 2021, 11:08
21 Feb 2021, 11:08
Solution:
\(-5^4^x\) will always yield a positive value. Thus, we need (9+x) to be even as well, which means x is odd.
Approach 1:
Either you could plug in the answer options and get the answer as 3
Approach 2:
\(-5^4^x=5^(^9^+^x^)\)
As both the sides have equal value and the powers even
4x=9+x
3x=9
x=3
IMO C
Hope this helps!
\(-5^4^x\) will always yield a positive value. Thus, we need (9+x) to be even as well, which means x is odd.
Approach 1:
Either you could plug in the answer options and get the answer as 3
Approach 2:
\(-5^4^x=5^(^9^+^x^)\)
As both the sides have equal value and the powers even
4x=9+x
3x=9
x=3
IMO C
Hope this helps!
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Re: If (-5)^(4x) = 5^(9 + x) and x is an integer, what is the value of x ?
[#permalink]
21 Feb 2021, 11:53
21 Feb 2021, 11:53
Carcass wrote:
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
Carcass
I tried editing it but couldn't. Can you please put \(4x\) and \((9 + x)\) in powers.
