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If n = 10^10 and n^n = 10^d, what is the value of d?
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22 Feb 2021, 09:53
22 Feb 2021, 09:53
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If \(n = 10^{10}\) and \(n^n = 10^d\), what is the value of \(d\)?
A. \(10^3\)
B. \(10^{10}\)
C. \(10^{11}\)
D. \(10^{20}\)
E. \(10^{100}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(10^3\)
B. \(10^{10}\)
C. \(10^{11}\)
D. \(10^{20}\)
E. \(10^{100}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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If n = 10^10 and n^n = 10^d, what is the value of d?
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22 Feb 2021, 10:13
22 Feb 2021, 10:13
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Carcass wrote:
If \(n = 10^{10}\) and \(n^n = 10^d\), what is the value of \(d\)?
A. \(10^3\)
B. \(10^{10}\)
C. \(10^{11}\)
D. \(10^{20}\)
E. \(10^{100}\)
A. \(10^3\)
B. \(10^{10}\)
C. \(10^{11}\)
D. \(10^{20}\)
E. \(10^{100}\)
Good Question Carcass
\(n^n = 10^d\)
\((10^{10})^n = 10^d\) ...................... [Since, \(n = 10^{10}\)]
\(10^{10n} = 10^d\)
When the bases are equal, powers are equal
\(10n = d\)
\((10)(10)^{10} = d\)
\(10^{1+10} = d\)
\(10^{11} = d\)
Hence, option C
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If n = 10^10 and n^n = 10^d, what is the value of d?
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22 Feb 2021, 10:25
22 Feb 2021, 10:25
1
Carcass wrote:
If \(n = 10^{10}\) and \(n^n = 10^d\), what is the value of \(d\)?
A. \(10^3\)
B. \(10^{10}\)
C. \(10^{11}\)
D. \(10^{20}\)
E. \(10^{100}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(10^3\)
B. \(10^{10}\)
C. \(10^{11}\)
D. \(10^{20}\)
E. \(10^{100}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Key property: \((b^x)^y = b^{xy}\)
If \(n = 10^{10}\), then \(n^n = (10^{10})^{(10^{10})} = 10^d\)
At this point, it helps to compare \((10^{10})^{(10^{10})}\) with \((b^x)^y\)
We can see that \(b \) \( = 10\), \(x \) \( = 10\) and \(y \) \( = 10^{10}\)
This means \(xy\) \(= (10)(10^{10})=(10^1)(10^{10})= 10^{11}\)
In other words: \((10^{10})^{(10^{10})} = 10^{(10^{11})} = 10^d\)
So, \(d=10^{11}\)
Answer: C
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