Question

7. Determinati multimea solutiilor ecuatiei log de x ( 6x - 5 ) = 2

Answer 1

[tex]log_x (6x-5)=2 \\ log_x (6x-5)=2 log_{x}x \\ log_x (6x-5)=log_{x}x^2 \\ 6x-5= x^{2} \\ - x^{2} +6x-5=0 |*(-1) \\ x^{2} -6x+5=0 \\ \Delta= b^{2}-4ac=36-4*1*5=36-20=16 \\ x_{1}= \frac{-b- \sqrt{\Delta} }{2a}= \frac{6-4}{2}= \frac{2}{2}=1\\ x_{2}= \frac{-b+\sqrt{\Delta} }{2a}= \frac{6+4}{2}= \frac{10}{2}=5[/tex]
S={1, 5}