Question

Se considera functia f:R->R, f(x)=log in baza x+2 din 4-x. Rezolvați ecuatia f(x)=2.​ Va rog, am nevoie urgentă!

Answer 1

$\log_{x+2}(4-x)=2$

Conditii de existenta:

$x+2>0\Rightarrow x>-2\\x+2\neq1\Rightarrow x\neq-1\\4-x>0\Rightarrow x<4\\\Rightarrow x\in(-2,4)\backslash\{1\}$

$\log_{x+2}(4-x)=2\\4-x=(x+2)^2\Rightarrow4-x=x^2+4x+4\Rightarrow x^2+5x=0\Rightarrow x(x+5)=0\Rightarrow (x=0\text{ sau }x+5=0)\\x+5=0\Rightarrow x=-5\text{ nu apar\c tine intervalului}\\\matcal{S}={0}$