Solve for
x, if:
3
x
x
x = 3
An algebraic solution is sought!
Substitute x^(x^(x^3)) for the three in the exponent to get:
x^(x^(x^(x^(x^(x^3))))) = 3
x^(x^(x^(x^(x^(x^(x^(x^(x^3)))))))) = 3
And repeat ad infinitum to get an infinite power tower:
x^(x^(x^(x^(x^(x^(x^(x^(x^(.........))))))))) = 3
Now the exponent of the bottom x is identical to the entire expression, so 3 can be substituted to yield x^3 = 3
The value x = cbrt(3) is the solution to all of the equations.
Power Tower
