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24 Feb 2024, 02:54
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C
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Difficulty:
55%
(hard)
Question Stats:
64% (01:12) correct
36%
(01:15)
wrong
based on 968
sessions
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Date
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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 14245 times ]
Attachment:
Screenshot 2024-02-24 152403.png [ 526.56 KiB | Viewed 14245 times ]
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.
01 Jul 2024, 23:55
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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.
Watch this solution to see it in action.
