Question

Hei, ajutați-mă, vă rog !

Log la x+2( 15+2x -x la 2)

Answer 1

$\it log_{x+2}(15+2x-x^2)$

$\it x+2\ \textgreater \ 0, \ \ x+2\neq1 \Longrightarrow x \neq -1$

Obținem x ∈ (-2,  -1) ∪ (-1,  ∞)      (1)

[tex]\it 15+2x-x^2 \ \textgreater \ 0 \Leftrightarrow x^2-2x-15\ \textless \ 0 \Leftrightarrow x^2-2x+1-16\ \textless \ 0 \Leftrightarrow \\\;\\ \Leftrightarrow (x-1)^2 -4^2\ \textless \ 0 \Leftrightarrow (x-1-4)(x-1+4) \ \textless \ 0 \Leftrightarrow \\\;\\ \Leftrightarrow (x-5)(x+3) \ \textless \ 0 \Leftrightarrow x \in (-3,\ 5) \ \ \ \ (2)[/tex]

$\it (1),\ (2) \Rightarrow D = (-3,\ 5) \backslash \{-1\}$