x = (√x)^(√x) x = (x^(1/2))^(√x) x = x^(1/2 * √x) x = x^((√x)/2) Since x > 0, take the log of both sides: log x = log(x^((√x)/2)) log x = ((√x)/2) * log x log x - ((√x)/2) * log x = 0 log x * (1 - ((√x)/2)) = 0 Therefore, log x = 0 x = 1 or 1 - ((√x)/2) = 0 (√x)/2 = 1 √x = 2 x = 2² x = 4 Solution: x ∈ {1, 4}.
(x ➖ 2x+2).
x = (√x)^(√x)
x = (x^(1/2))^(√x)
x = x^(1/2 * √x)
x = x^((√x)/2)
Since x > 0, take the log of both sides:
log x = log(x^((√x)/2))
log x = ((√x)/2) * log x
log x - ((√x)/2) * log x = 0
log x * (1 - ((√x)/2)) = 0
Therefore,
log x = 0
x = 1
or
1 - ((√x)/2) = 0
(√x)/2 = 1
√x = 2
x = 2²
x = 4
Solution: x ∈ {1, 4}.