+2440 Well, Mr. Blarney Bag, like usual, you are wrong. This calculator can display a fully resolved mantissa of at least 2048 digits. You just have to know how to use it. I could explain it but you need to be smarter than the machine to understand it. So, that leaves you out.
This equation is a solution to the probability of two persons NOT sharing the same birthday (date) in a group of thirty persons.
Alan elaborates on the equation (not the probability), here.
And he presents a much more clear method of entering it into the calculator, here.
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Correction on comment
This equation is a solution to the probability of two persons NOT sharing the same birthday (date) in a group of thirty persons.
The original read:
This equation is a solution to the probability of two persons sharing the same birthday (date) in a group of thirty persons.
1-(npr(365,(365-335))/365^30) is the solution to the probability of two persons sharing the same birthday (date) in a group of thirty persons.
+2440 Actually, they are not interpreted same. Each interpretation gives a different solution for x.
As Hectictar pointed out:
Sir Alan’s interpretation is: 4^(2^x) + 2^(2^x) = 56
And Sir CPhill interpretation is: (4^2)^x + (2^2)^x = 56
Sir Alan’s is interpretation is exactly the same as the asked question. (This follows power-tower convention, where stacked powers are multiplied from right to left or from the top down, and the resultant product becomes the exponent to the base number.)
Sir CPhill’s solution starts with the base then increments the value by each ascending power.
The solutions for these interpretations give different results for the value of x.
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\(\text{For Sir Alan's solution}\\ x = log_2 (log_2(7))\\ x \approx 1.4892114692\\ \text{ }\\ \text{For Sir CPhill’s solution}\\ 2x = \dfrac {log (7) } { log (2)}\\ x= \dfrac {log (7)/ log (2)}{(2)}\\ x\approx 1.4036774610\\ \)
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Sir Alan notes the calculator input error of the questioner; however, the questioner may have correctly entered this into the site calculator
(4^2^log(log(7, 2), 2)) + (2^2^log(log(7 , 2), 2) )
The calculator would interpret it as
(4^2)^(log(log(7, 2), 2)) + (2^2)^log(log(7 , 2), 2))
The site’s calculator does NOT follow hierarchal convention in interpreting stacked powers.
Here is an elaboration on this issue:
Use of parenthesis to, in this case, force proper hierarchal convention
(4^(2^log(log(7, 2), 2)) + (2^(2^log(log(7 , 2), 2)
gives 56 as the result.
Which value of x is correct? Only the asker’s hairdresser knows for sure.
