Question

sa se rezolve in R
log in baza 3 din (x+2)=log in baza 3 din x^2

Answer 1

   
[tex]\displaystyle\\ \log_{3}(x+2)=\log_3(x^2)\\ \text{Conditii:}\\ x+2 \ \textgreater \ 0~~~\Rightarrow ~~~ x\ \textgreater \ -2\\ x^2 \ \textgreater \ 0~~~\Rightarrow ~~~x\ \neq 0\\ ==\Longrightarrow~~x\in (-2;~0)\bigcup(0;~+\infty)\\\\ \text{Avem egalitate intre doi logaritmi in aceeasi baza}\\\\ x+2=x^2\\\\ x^2-x-2=0\\\\ x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{1\pm\sqrt{1+4\cdot 2}}{2} =\frac{1\pm\sqrt{9}}{2}=\frac{1\pm3}{2}\\\\ x_1=\frac{1-3}{2}=\frac{-2}{2}=\boxed{-1}\\\\ x_2=\frac{1+3}{2}=\frac{4}{2}=\boxed{2}[/tex]