Question

Cum se rezolva 3 lg la 2x-4lgx+3=0 ?? Va rog urgent.

Answer 1

[tex]3\lg ^2x-4\lg x+1=0\\ \text{Conditii de existenta:} x\ \textgreater \ 0\\ Notam: \lg x=t\\ 3t^2-4t+1=0\\ \Delta=16-12=4\Rightarrow \sqrt{\Delta}=2\\ t_1=\dfrac{4+2}{6}=1\ \textgreater \ 0\\ t_2=\dfrac{4-2}{6}=\dfrac{1}{3}\ \textgreater \ 0\\ i)\lg x=1\Rightarrow x_1=10\\ ii)\lg x=\dfrac{1}{3}\Rightarrow x_2=\sqrt[3]{10}\\ S:x\in \{10,\sqrt[3]{10} \}[/tex]