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gmatophobia
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (01:10) correct
34%
(01:14)
wrong
based on 1459
sessions
History
Date
Time
Result
Not Attempted Yet
If x is a real number and \(4^{(4^{4})} = 2^{(2^x)}\), what is the value of x ?
A. 7
B. 8
C. 9
D. 16
E. 256
_________________
A. 7
B. 8
C. 9
D. 16
E. 256
Screenshot 2024-02-24 152403.png [ 526.56 KiB | Viewed 18720 times ]
Attachment:
Screenshot 2024-02-24 152403.png [ 526.56 KiB | Viewed 18720 times ]
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
If x is a real number and \(4^{(4^{4})} = 2^{(2^x)}\), what is the value of x ?
A. 7
B. 8
C. 9
D. 16
E. 256
Answer: C.
_________________
A. 7
B. 8
C. 9
D. 16
E. 256
\(4^{(4^{4})} = 2^{(2^x)}\)
\((2^2)^{((2^2)^{4})} = 2^{(2^x)}\)
\((2^2)^{(2^8)} = 2^{(2^x)}\)
\(2^{2*2^8} = 2^{(2^x)}\)
\(2^{2^9} = 2^{(2^x)}\)
\( x = 9\)
\((2^2)^{((2^2)^{4})} = 2^{(2^x)}\)
\((2^2)^{(2^8)} = 2^{(2^x)}\)
\(2^{2*2^8} = 2^{(2^x)}\)
\(2^{2^9} = 2^{(2^x)}\)
\( x = 9\)
Answer: C.
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This is a question that tests your very basic understanding of exponents and relies on your ability to neatly organize your work so that you do not make mistakes.
Watch this solution to see it in action.
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General Discussion
Posts: 9
I also get 16 as answer and can’t really figure out why it is 9. Can someone pls explain? I’m surely making a mistake with exponential properties, but don’t know which one.
Thanks!
Posted from my mobile device
Thanks!
Posted from my mobile device
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 09 Sep 2026
Posts: 3,174
Location: India
Concentration: Strategy, Leadership
Posts: 3,174
gmatophobia
Francesco_8167 Check if this helps
\( 4^{4} = 4 * 4 * 4 * 4 = 16 * 16 = 256\)
\(4^{(4^{4})} = 4^{256} = (2^2)^{256} = 2^{2*256} = 2^{512}\)
\(512 = 2^9\)
Hence, the answer is C
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Oppenheimer1945
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4^256=2^2^x
=> 2^2.256=2^2^x
=> 2.256=2^x
=>512=2^x
As 1024=2^10, 512=2^9
x=9
=> 2^2.256=2^2^x
=> 2.256=2^x
=>512=2^x
As 1024=2^10, 512=2^9
x=9
ablatt4
Joined: 18 Dec 2024
Last visit: 24 Sep 2025
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Location: United States (FL)
Concentration: Finance
Schools: Duke '26 Darden '26 Johnson '26 UNC '26
Schools: Duke '26 Darden '26 Johnson '26 UNC '26
Posts: 87
More than anything this is Order of Operations
4^(4^4)= 2(2^x)
4^256 = 2(2^x)
2^512= 2(2^x)
2^(2^9) = 2(2^x)
2^9=2^x
x=9
4^(4^4)= 2(2^x)
4^256 = 2(2^x)
2^512= 2(2^x)
2^(2^9) = 2(2^x)
2^9=2^x
x=9
gmatophobia
are there more questions of this type to practice?
gmatophobia
Ridhima29
Exponents and Roots of Numbers
Theory:
Questions
- Units digits, exponents, remainders problems
- Tough and tricky DS exponents and roots questions with detailed solutions
- Tough and tricky PS exponents and roots questions with detailed solutions
- Exponents PS Questions
- Roots PS Questions
Check below for more:
Hope this helps.
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gmatophobia
Responding to a pm:
Use the rules of exponents. We know that 4 = 2^2 so we should simplify the LHS.
\(4^{(4^{4})} = (2^2)^{(2^{2*4})} = 2^{(2^{9})}\)
\(2^{(2^x)}\) is the RHS
Hence x = 9
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