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2^199 + 2^199 = 2^X

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2^199 + 2^199 = 2^X [#permalink] New post 29 Aug 2003, 06:30
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Solve for X

2^199 + 2^199 = 2^X
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Sept 3rd

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 [#permalink] New post 29 Aug 2003, 06:48
yes, that is great!!

how about 3^199 + 3^199
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 [#permalink] New post 29 Aug 2003, 07:05
Surely, that must have been confusing. Here we go...

3^199 + 3^199 = 3^X
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 [#permalink] New post 29 Aug 2003, 07:30
mciatto wrote:
Surely, that must have been confusing. Here we go...

3^199 + 3^199 = 3^X


I don't even know if you can solve 3^199 + 3^199 = 2^X without a calculator i just didn't want to assume.

Anyway i'm really stumped on this one. The way i did the previous one was:-

2^199 + 2^199 = 2^X
2(2^199) = 2^X
2^199 = 2^X-1

Therefore X has to be 200. However this method does not work for the 3^199 question, unless i'm missing something, which would not be the first time.
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 [#permalink] New post 29 Aug 2003, 07:36
3^199 + 3^199 = 3^X

im not sure if we can solve that without a calculator... id do the following:

3^199 + 3^199=2*(3^199)=3^X

2=3^y, solving for y we get y=log2/log3

thus 2*(3^199)=3^(log2/log3)*(3^199)=3^(log2/log3+199)

x=log2/log3+199

i may be mistaken though...
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 [#permalink] New post 29 Aug 2003, 07:42
I think this is obviously too complicated for the GMAT, but it was worth a shot.

All I can say is that

3^199 + 3^199 = (2/3)* 3^200
I'm not sure if this equates to javropu's solution.
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 [#permalink] New post 29 Aug 2003, 07:47
I guess all that's for sure is 199<X<200.

Hopefully there would be one answer choice in that range :-D
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  [#permalink] 29 Aug 2003, 07:47
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2^199 + 2^199 = 2^X

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