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What is the value of (2^64)^(2^64)

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by firdaus117 » Wed Feb 24, 2010 12:38 pm
Take log to base 2 on both sides,

log 2^p=logd^d
p=d*log d
=2^64*log 2^64
=2^64*64
=2^64*2^6
=2^70
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by rayyogi » Wed Feb 24, 2010 1:17 pm
Of all the GMAT material that I covered, never came across "log" and its usage. Not sure if I missed it completely. Is there any other way to solve this without using "log"
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by analyst218 » Wed Feb 24, 2010 1:51 pm
i got the same question.. last week when i took the real test.
this is how i did it. (simplification)

[2^64]^[2^64] = 2^[64*2^64] = 2^[2^6 * 2^64] = 2^[2^70]
p=2^70

did u take it on 2/20?
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by rayyogi » Wed Feb 24, 2010 2:13 pm
I took the test on 2/16.

p=2^70 doesn't seem right.

As far as I can remember the highest number in the answer choices was around 1024. Other choices were 64, 128, 32 and some other small number (less than 1000) that I can't remember
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by analyst218 » Wed Feb 24, 2010 2:19 pm
it's right.
look at it this way.
think 2^64 as an integer, say X. then [2^64]^X would be 2^(64*X) right?
64 = 2^6 and plug in 2^64 in X then you get 2^64 * 2^6 = 2^70. thus p=2^70.
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by rayyogi » Wed Feb 24, 2010 7:39 pm
Seems logical. May be its correct.

Thank you.
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