Karnage Posted October 20, 2005 Share Posted October 20, 2005 Here's problem I need help on. It relies mainly on one's intuition and intelligence. Can anone hlep me out and give a full, good explanation? Every number can be represented in the standard form such as [math]\frac{100}{3} = 3.33 * 10^1[/math]. In this form the number [math]x = a * 10^N[/math], where [math]1<a<10[/math], while N is an integer exponent. Find the standard form for [math]x = 1234^1234[/math]. Include only three leading decimals in your answer, as in the previous example. Link to comment Share on other sites More sharing options...
Karnage Posted October 20, 2005 Author Share Posted October 20, 2005 [math]x = 1234^1234[/math] heehee sry im kinda new to latex Link to comment Share on other sites More sharing options...
Karnage Posted October 20, 2005 Author Share Posted October 20, 2005 rrrrrrrr its suposed to be x = 1234^1234 (sumthin's up with the coding) Link to comment Share on other sites More sharing options...
ecoli Posted October 20, 2005 Share Posted October 20, 2005 did you mean [imath] 1234^{1234} ? [/imath] edit: you need a { and } around the exponent, or it'll only read the first number. Link to comment Share on other sites More sharing options...
Karnage Posted October 20, 2005 Author Share Posted October 20, 2005 [math]x = 1234 ^ 1234 [/math] express that in the terms stated in the problem above. Link to comment Share on other sites More sharing options...
ecoli Posted October 20, 2005 Share Posted October 20, 2005 I think you're talking about scientific notation, correct? you want [imath]1234^{1234} [/imath] in sci not? Link to comment Share on other sites More sharing options...
Karnage Posted October 20, 2005 Author Share Posted October 20, 2005 yes i want it in the form of notation as shown in the previous example Link to comment Share on other sites More sharing options...
ecoli Posted October 20, 2005 Share Posted October 20, 2005 I think it might be [imath] 1.234 * 10^{3702} [/imath] but don't take my word for it. Link to comment Share on other sites More sharing options...
Karnage Posted October 20, 2005 Author Share Posted October 20, 2005 Do you have an explanation? Link to comment Share on other sites More sharing options...
cosine Posted October 20, 2005 Share Posted October 20, 2005 Do you have an explanation? [math]1234^{1234}=10^{x}[/math] [math]1234(\log(1234))=x[/math] [math]1234(\log(1234)) = 3814.6829070663730305378590465079...[/math] [math]1234^{1234} = (10^{3814})(10^{.6829070663730305378590465079...})[/math] [math]10^{.6829070663730305378590465079...} = 4.8184467781382543701667186035719...[/math] [math]1234^{1234} = 4.8184467781382543701667186035719... * 10^{3814}[/math] Sorry about the large amount of digits, I'm sort of paranoid about inaccurate decimal representations, but I was too tired to figure out a probably obvious exact form. But anyway, hope this helps. Link to comment Share on other sites More sharing options...
Karnage Posted October 20, 2005 Author Share Posted October 20, 2005 Yea I was thinking the same method and got the same answer. I was hoping for a more systematic and exact way of figuring it out though. But thnx anyway Link to comment Share on other sites More sharing options...
Karnage Posted November 3, 2005 Author Share Posted November 3, 2005 [math]1234^{1234}[/math] Link to comment Share on other sites More sharing options...
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