how many integer s n is n^2=2^n none 1 2 3 more than 3

Question

how many integer s n is n^2=2^n


none
1
2
3
more than 3

chiragr · Answer

yep it's two, I did not have tenacity to go beyond 0, +-1 and 2...

mrmikec · Answer

I got two also

-2^2 = 4 but 2^-2 = 1/4
-1^2 = 1 but 2^-1 = 1/2
0^2 = 0 but 2^0 = 1
1^2 = 1 and 2^1 = 2

Fig · Answer

Get 2 as well.

n 0 and it could not be equal to n^2.

By trying 2 and 4 for n we get already the 2 values

Is it other values possibles?
n^2 = 2^n with n > 0
 ln(n^2) = ln (2^n)
 2*ln(n) = n*ln(2)
 ln(n) / n = ln(2) / 2

f(x) = ln(x) / x is not a kind of oscillating equation on a limit value. When x is positve and inscreases, f(x) tends fast to 0.

Actually, i would like to say that f(x) passes the value ln(2) / 2 at x=2, stays a few upper the value ln(2)/2 by going to a maximum value and tends to 0 by passing back on the value of ln(2) / 2 at x=4.

how many integer s n is n^2=2^n none 1 2 3 more than 3

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