Math question for those w/ Calc background

[AStudent]

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what is 4^(3,100,000,000)? I know there was a formula like n(ln n)-n or something like that to approximate VERY large exponents.

FYI: I'm trying to figure out the theoretical number of different possible combinations in the human genome. (yes, i know that humans share alot of homologous sequences so spare me the genetics lession)

 

[penguinophile]

what is 4^(3,100,000,000)? I know there was a formula like n(ln n)-n or something like that to approximate VERY large exponents.

FYI: I'm trying to figure out the theoretical number of different possible combinations in the human genome. (yes, i know that humans share alot of homologous sequences so spare me the genetics lession)

The formula you're thinking of won't help you. That is sterling's approximation, which involves the approximation of large factorials.

 

[mercaptovizadeh]

what is 4^(3,100,000,000)? I know there was a formula like n(ln n)-n or something like that to approximate VERY large exponents.

FYI: I'm trying to figure out the theoretical number of different possible combinations in the human genome. (yes, i know that humans share alot of homologous sequences so spare me the genetics lession)

It's roughly 10^1866385973, or more roughly, 10 to the 2 billion, or googol^20000000.

 

[represent_CV]

just say millions and millions and millions and millions...i think that is close enuf

 

[americanpierg]

24e^9tiranglesmileyface- delta pi

 

[americanpierg]

just say millions and millions and millions and millions...i think that is close enuf

thats only 4 million...not close at all

 

[AStudent]

It's roughly 10^1866385973, or more roughly, 10 to the 2 billion, or googol^20000000.

Any reasoning behind this?

 

[mercaptovizadeh]

Any reasoning behind this?

Well, if you're changing bases, just say:

4^3100000000 = 10^x

ln(4^3100000000) = ln(10^x)

3100000000*ln4 = x*ln10

x = (3100000000*ln10)/ln4 = 1866385973

ergo its on the order of 10^1866385973