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If \(x^x = 2^{2048}\), what is the value of \(x\)?
A. \(28\)
B. \(128\)
C. \(256\)
D. \(512\)
E. \(1024\)
A. \(28\)
B. \(128\)
C. \(256\)
D. \(512\)
E. \(1024\)
20 Feb 2023, 10:58
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Bookmarks
Official Solution:
If \(x^x = 2^{2048}\), what is the value of \(x\)?
A. \(28\)
B. \(128\)
C. \(256\)
D. \(512\)
E. \(1024\)
To answer the question, we need to express \(2^{2048}\) such that the base and the power are the same.
\(2^{2048}=2^{2*1024}=4^{1024}=4^{2*512}=16^{512}=16^{2*256}=256^{256}\).
\(x=256\).
Answer: C
If \(x^x = 2^{2048}\), what is the value of \(x\)?
A. \(28\)
B. \(128\)
C. \(256\)
D. \(512\)
E. \(1024\)
To answer the question, we need to express \(2^{2048}\) such that the base and the power are the same.
\(2^{2048}=2^{2*1024}=4^{1024}=4^{2*512}=16^{512}=16^{2*256}=256^{256}\).
\(x=256\).
Answer: C
