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# The Hardest Math Problem Ever

Registered User Posts: 240 Junior Member
edited October 2012
"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.
Post edited by obsessedAndre on
«1

## Replies to: The Hardest Math Problem Ever

• Registered User Posts: 34 Junior Member
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..!
• Registered User Posts: 240 Junior Member
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.
• Registered User Posts: 248 Junior Member
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.
• Registered User Posts: 3,164 Senior Member
you should do what most people do... SKIP or GUESS
• Registered User Posts: 240 Junior Member
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.
• Registered User Posts: 777 Member
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
• Registered User Posts: 240 Junior Member
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?
• Registered User Posts: 119 Junior Member
BestMiler, that's the kind of terrible advice that comes from people who don't do well.
• Registered User Posts: 3,164 Senior Member
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
• Registered User Posts: 777 Member
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 :p. i didnt know you needed the smallest number possible though
• Registered User Posts: 1 New Member
or you could just use iteration and get the value quicker
• Registered User Posts: 9 New Member