Question

Rezolvati in R
a)log in baza 0,1 din (3x-1)=-1
b)log in baza radincal din 2 din( x ^2-3x)=6

Answer 1

[tex]a)\log_{0,1}(3x-1)=-1\\ 3x-1=0,1^{-1}\\ 3x-1=\left(\frac{1}{10}\right)^{-1}\\ 3x-1=10\\ 3x=11\\ x=\frac{11}{3}\\ \\ b)\log_{\sqrt2}(x^2-3x)=6\\ \log_{2^{\frac{1}{2}}}(x^2-3x)=6\\ 2\log_{2}(x^2-3x)=6\\ \log_{2}(x^2-3x)=3\\ x^2-3x=8\\ x^2-3x-8=0\\ \Delta=9+4\cdot 8=41\Rightarrow \sqrt{\Delta}=\sqrt{41}\\ x_1=\frac{3+\sqrt{41}}{2}\\ x_2=\frac{3-\sqrt{41}}{2}[/tex]