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R = 3^81, R^R = 3^S, S = ?
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Updated on: 16 Aug 2012, 01:52
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\(R = 3^{81}\) \(R^R = 3^S\) \(S = ?\) A. 3 B. 81 C. 3^81 D. 3^85 E. 3^87
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Originally posted by ksharma12 on 13 Apr 2010, 14:23.
Last edited by Bunuel on 16 Aug 2012, 01:52, edited 1 time in total.
Edited the question and added the OA.




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Re: 700+ Level exponent question
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13 Apr 2010, 23:37
\(R = 3^{81}\) \(R^R = 3^{81*R}\) \(R^R = 3^{81*3^{81}}\) \(R^R = 3^{3^4*3{^81}}\) \(R^R = 3^{3^{4+81}}\) \(R^R = 3^{3^{85}}\) thus S = 85
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Re: 700+ Level exponent question
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13 Apr 2010, 15:23
not really sure I'm doing this right but anywho...
using simpler numbers if R = 2^2 Then R^R = 2^8
Difference of 6 on the exponents
So 81 + 6 = 87
E
curious if that makes any sense.



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Re: 700+ Level exponent question
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13 Apr 2010, 18:09
Don't get freaked by the number of exponents.
((x)^(y))^(z) = (x)^(yz) property
so (3^81)^(3^81) = 3^(81*3^81)
and 3^4 =81
x^y*x^z = x^(y+z)
so 3^(3^4*3^81) = 3^(3^85)
thus s = 3^85
If someone could tell me how to do superscripts I could possibly make this easier to read.



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Re: 700+ Level exponent question
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15 Aug 2012, 08:46
This problem can be solved very quickly using logarithm (although it is not in the syllabus of GMAT) R=3^81 log (R) = 81 log 3 And since, R^R = 3^s therefore, R log R = s log 3 Now substituting the value of log R from eqn. 1, R X (81 log 3) = s log 3 Hence, s = 3^81 X 3^4 = 3^ 85



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Re: 700+ Level exponent question
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15 Aug 2012, 23:18
One more way  Exponential  Given  R = 3^81.....(a) R^R = 3^S R = 3 ^(S/R)............(b) (a) = (b) we get S/R = 81 i.e. S=81R i.e. S=81 * 3^81 hence S = 3^4 + 3^81 = 3^85
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Re: R = 3^81, R^R = 3^S, S = ?
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27 Feb 2014, 20:55
Given that R = 3^81 Powering both sides by R R^R = 3^81R............... (1) Already given that R^R = 3^S......... (2) Equating (1) & (2) S = 81R = 3^4 . 3^81 = 3^85 = Answer = D
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Re: R = 3^81, R^R = 3^S, S = ?
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28 Feb 2014, 22:36
here's another way.... R^R = (3^81)^(3^81) > (27^27)^(27^27) (27)^(27^28) (3^3)^[3^(28*3)] 3^[3^(1+28*3)] 3^(3^85)
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R = 3^81, R^R = 3^S, S = ?
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03 Oct 2015, 07:43
R=3^81 given
R^R=3^S given
=> (3^81)^R = 3^S => 3^(81R) = 3^S => 81R = 3^S => 3^4 x 3^81 = 3^S => s=52
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Re: R = 3^81, R^R = 3^S, S = ?
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30 Nov 2016, 17:36
ksharma12 wrote: \(R = 3^{81}\)
\(R^R = 3^S\)
\(S = ?\)
A. 3 B. 81 C. 3^81 D. 3^85 E. 3^87 \(R = 3^{81}\)So, \(R^R = (3^{81})^{3^{81}}\) [replaced R with 3^81]\(= (3^{3^4})^{3^{81}}\) [rewrote 81 as 3^4]\(= 3^{3^{85}}\) [applied power of power rule AND product rule]So, \(3^{3^{85}} = 3^S\) So, \(S = 3^{85}\) Answer: E
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Re: R = 3^81, R^R = 3^S, S = ?
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