Question

3la puterea 2x-2*3la putereax-3=10 ajutatima va rog mult.....multumesc:*

Answer 1

   
[tex]\displaystyle\\ 3^{2x}-2\cdot 3^x-3=10\\ (3^x)^2-2\cdot 3^x-3-10=0 \\ (3^x)^2-2\cdot 3^x-7=0 \\ \text{Notam: }t=3^x\\ t^2-2t-7=0\\\\ t_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\\\\ \frac{2\pm\sqrt{4+28}}{2}=\frac{2\pm \sqrt{32}}{2}=\frac{2\pm 4\sqrt{2}}{2}=1\pm 2\sqrt{2}\\\\ t_1=1+2\sqrt{2}~\Longrightarrow~ 3^x=1+2\sqrt{2}~\Longrightarrow~ \boxed{x=\log_3(1+2\sqrt{2})}\\ \\ t_2=1-2\sqrt{2}~\Longrightarrow~ 3^x=1-2\sqrt{2}~\Longrightarrow~ \boxed{x=\log_3(1-2\sqrt{2})} [/tex]