An intuitive problem!!!!!

[Karnage]

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 $\frac{100}{3} = 3.33 * 10^1$. In this form the number $x = a * 10^N$, where $1<a<10$, while N is an integer exponent. Find the standard form for $x = 1234^1234$. Include only three leading decimals in your answer, as in the previous example.

[Karnage]

$x = 1234^1234$

 

heehee sry im kinda new to latex

[Karnage]

rrrrrrrr its suposed to be x = 1234^1234 (sumthin's up with the coding)

[ecoli]

did you mean [imath] 1234^{1234} ? [/imath]

 

edit: you need a { and } around the exponent, or it'll only read the first number.

[Karnage]

$x = 1234 ^ 1234$

express that in the terms stated in the problem above.

[ecoli]

I think you're talking about scientific notation, correct?

you want [imath]1234^{1234} [/imath] in sci not?

[Karnage]

yes i want it in the form of notation as shown in the previous example

[ecoli]

I think it might be [imath] 1.234 * 10^{3702} [/imath] but don't take my word for it.

[Karnage]

Do you have an explanation?

[cosine]

  Karnage said:

Do you have an explanation?

 

$1234^{1234}=10^{x}$

 

$1234(\log(1234))=x$

 

$1234(\log(1234)) = 3814.6829070663730305378590465079...$

 

$1234^{1234} = (10^{3814})(10^{.6829070663730305378590465079...})$

 

$10^{.6829070663730305378590465079...} = 4.8184467781382543701667186035719...$

 

$1234^{1234} = 4.8184467781382543701667186035719... * 10^{3814}$

 

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.

[Karnage]

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

[Karnage]

$1234^{1234}$