Determine all possible real values of n that satisfy this equation:
nn = 81√6/32.
It looks like the answer is 2.25. The Desmos graph shows that a value of 81*sqrt(6)/32 is well within the area of n^n where it is monotonically increasing, with the domain < 1 never getting so high; therefore the solution is unique.
>> eq=n^n==81*sqrt(6)/32
eq =
n^n == (81*2^(1/2)*3^(1/2))/32
>> digits 1000
>> vpasolve(eq)
ans =
2.25
>>
Wolfram alpha shows, when asked for "more digits" in its response to a request for the solution, shows
n = e^W(-9/2 (log(2) - log(3)))˜2.250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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Posted by Charlie
on 2024-10-01 09:31:22 |
computer solution
