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by adthedaddy » Thu Sep 24, 2015 7:27 pm
Is 3^m less than 2000 ?

1. 3^m+1 > 2000
2. 3^m-1 = 3^m-486

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by Matt@VeritasPrep » Fri Sep 25, 2015 12:57 am
S1::

3��¹ = 3� * 3, so we have

3� * 3 > 2000, or

3� > (2000/3)

Assuming integers -- NOT a reasonable assumption here, but I'm guessing the author intended this -- this gives m ≥ 6. If m = 6, then 3� < 2000. If m ≥ 7, then 3� > 2000. NOT SUFFICIENT.

S2::

I'm assuming you mean

3��¹ = 3� - 486

which is

486 = 3� - 3��¹, or

486 = 3��¹ * (3 - 1), or

243 = 3��¹

So (m - 1) = 5, and m = 6. This gives us one and only one value, so it is sufficient to answer the question (YES, 3� = 729, which is < 2000.)
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