Question

Solve:
x^(x^(x^(x^(x^....)))) = 3

Answer 1

x^3 = 3

u see.. its just this.
solve for x now

Answer 2

we have this simplified form :
x^3 = 3
solve for x..
(assuming x tends to infinyt)

Answer 3

infinity**

Answer 4

Thats right. But x have not only one solutions.

Answer 5

how about x^(x^3) = 3
or x^3 (ln x) = ln 3

i dont know how we can solve this one :
but this will surely give another value of x

Answer 6

Not x^(x^3) = 3.
x^3 * x^3 =3
Another value of x is 3^(1/9)
And actually there are infinite number of solutions of x. out of which x^(1/3) is the largest.

Answer 7

x^3 . x^3 = 3 ??? you sure ???
i hope its not (x^x).(x^x)..... ?

Answer 8

Sorry. My mistake

Answer 9

hmm,,so that requires the knowledge of interpolation to solve for further values of x.
and yes,,must be infinite values of x

Answer 10

x^(3^3)

Answer 11

x^(3^(3^(3)))

Answer 12

and so on

Answer 13

if you have already substitued that much part to be 3..you have nothing left(ofcorse)
i mean 3^3 is not valid..and also further ones are not valid

Answer 14

u asking if this can look like this :
\[\huge{x^{x^3} = 3 }\]

?

Answer 15

infinity never ends

Answer 16

your logic is wrong buddy @sauravshakya ,,please re-think.. zabardasti solve kar rahe ho..

Answer 17

3^(1/9) and 3^(1/27) both are valid

Answer 18

ofcorse not!! hmm,,

Answer 19

i think she is correct.. @shubhamsrg ..

can you explain my above expression... im confused after putting that :(

Answer 20

x^(x^3) = 3..yes thats fine..
and not x^(3^3) <---this is humbug! :P

Answer 21

i mean, her question is valid... 1/9 is ofcourse not equal to 1/27 !!

Answer 22

ahh.. i see now... thanks @shubhamsrg ;)

Answer 23

I will return.....
With a proof

Answer 24

hmmm..

Answer 25

The proof is simple.
Since x^(x^(x^(x^(x^....)))) = 3, s^[x^(x^(x^(x...))))] =3, or x^3 =3