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 02-11-2006, 09:14 PM #1 Junior Member   Join Date: Jul 2005 Posts: 237 The Hardest Math Problem Ever "Find x > 3 such that ln(x) < x^(0.1)" How do you solve this type of problem? I plugged it into my TI-89 solver and didn't get anything. As a hint, the number is unbelievably huge. Reply
 02-11-2006, 11:20 PM #2 Junior Member   Join Date: Jan 2006 Posts: 34 is there any other criteria, like x has to be an integer? because if it is just x> 3, then stuff like x = 3.04 could technically work in that equation... but yeah there must be a huge number greater than 3.05 that satisfies that equation, 'cept i have noo clue how to find it xD.. maybe there's a geometric sequence with the amount each value's increase is decreasing x__o if that makes anY sense..! Reply
 02-12-2006, 12:05 AM #3 Junior Member   Join Date: Jul 2005 Posts: 237 Hmm.. you might be barking up the right tree with the series idea. The problem doesn't say n must be an integer, but I guess what they mean is n > 3.xxxx... because you're right 3.05 would work. Reply
 02-12-2006, 12:34 AM #4 Junior Member   Join Date: Jan 2006 Posts: 240 I got X = 3.0597 also. I graphed ln(x) and x^.1 and then looked for the interesection which was (3.0597, 1.1183). Therefore, isn't 3.05 the answer? If you plug it back in, it works. Reply
 02-12-2006, 01:37 AM #5 Senior Member   Join Date: Feb 2006 Location: in a far away galaxy Posts: 1,596 you should do what most people do... SKIP or GUESS Reply
 02-12-2006, 02:42 PM #6 Junior Member   Join Date: Jul 2005 Posts: 237 Yes, 3.06 works in the equation, but it's not the answer they're looking for which is an integer and EXTREMELY HUGE. It's a free response question, so you can't guess. I'm wondering how on earth they expect you to figure this out... Just in case anyone's panicking, this is way beyond anything on the SAT or SAT II. Reply
 02-12-2006, 02:53 PM #7 Member   Join Date: Nov 2005 Location: Swarthmore Posts: 659 5 X 10^15 works lol ln(5 X 10^15) = 36.14821... (5 X 10^15)^.1 = 37.1447... every number higher than that works too so i guess thats prolly not right Reply
 02-12-2006, 02:57 PM #8 Junior Member   Join Date: Jul 2005 Posts: 237 Andrassy, you're incredible! The actual answer is n => 3.431 x 10^15, so you're answer is correct although it is not the smallest correct answer. You got the decimal places right, though! What made you think of anything x 10^15? Did you just guess and check? Reply
 02-12-2006, 03:51 PM #9 Junior Member   Join Date: Jan 2006 Posts: 118 BestMiler, that's the kind of terrible advice that comes from people who don't do well. Reply
 02-12-2006, 04:15 PM #10 Senior Member   Join Date: Feb 2006 Location: in a far away galaxy Posts: 1,596 i do well but if you cant get it, then what you can do in the SATS? Skipping it is the best choice rather than get it wrong Reply
 02-12-2006, 06:26 PM #11 Member   Join Date: Nov 2005 Location: Swarthmore Posts: 659 i just guessed it lol =( sorry i couldnt be of more help...i have no idea how to do it...it had to be a huge number so after i tried like 10000 i did like 50 x 10^10 no, 50 x 10^15 yay . i didnt know you needed the smallest number possible though Reply
 08-06-2007, 10:16 AM #12 New Member   Join Date: Aug 2007 Posts: 1 or you could just use iteration and get the value quicker Reply
 08-23-2007, 06:45 AM #13 New Member   Join Date: Aug 2007 Posts: 9 the answer is x>11ln0.1/1-(0.1)^11 Reply
 10-21-2010, 09:40 PM #14 New Member   Join Date: Oct 2010 Posts: 1 yeah umm sorry to burst you bubble but 0
 10-24-2010, 08:52 PM #15 Junior Member   Join Date: Oct 2010 Posts: 72 That's ridiculous. How can that be on the SAT? No SAT question - by Collegeboard regulations - needs a calculator to solve. This one obviously does. Reply

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