x^ log(2) (x) - 2 = 256 = 2^8
- Condiție de existență: x > 0
- logaritmam
log(2) (x ^ log(2) (x) - 2) = log(2) (2^8)
(log(2) (x) - 2 ) • log(2) (x) = 8 log(2) (2)
(log(2) (x) - 2) • log(2) (x) = 8
(t-2) • t = 8
t² - 2t - 8 = 0
t² - 4t + 2t - 8 = 0
t( t - 4 ) + 2( t - 4 ) = 0
( t + 2 )( t - 4 ) = 0
t1 = - 2 sau t2 = 4
log(2) (x) = t1
log(2) (x) = -2
x = 2^ - 2 = 1/2^2 = 1/4 > 0
sau
log(2) (x) = t2
log(2) (x) = 4
x = 2^4 = 16 > 0
S ={ 1/4 ; 16 }
