Question

Rezolvare completa la subpunctul c) ca sa inteleg cum se face, multumesc !

Answer 1

Explicație pas cu pas:

a)

$0*0= log_{2}( {2}^{0} + {2}^{0} ) = log_{2}(1 + 1) = log_{2}(2) = 1$

b)

$x*y = log_{2}({2}^{x} + {2}^{y}) \\ y*x = log_{2}({2}^{y} + {2}^{x}) \\ log_{2}({2}^{x} + {2}^{y}) =log_{2}({2}^{y} + {2}^{x}) \\ = > x*y = y*x$

=> legea "*" este comutativă

c)

$x*x = log_{2}({2}^{x} + {2}^{x}) = log_{2}(2 \times {2}^{x}) = log_{2}({2}^{x + 1}) = x + 1$

$(x*x)*x = log_{2}({2}^{x + 1} + {2}^{x}) = log_{2}(2 \times {2}^{x} + {2}^{x}) = log_{2}(3 \times {2}^{x}) = log_{2}(3) + log_{2}({2}^{x}) = log_{2}(3) + x$

$log_{2}(3) + x = 3 + log_{2}(3) = > x = 3$

x = 3