Question

Solve ${\log }_{x-2}(3x^2-x-1)>0$

Answer 1

Base must be positive and not equal to 1 i.e. x-2>0 ($\ne 1$)

For the required condition to be true,

If 1 > Base > 0 then 1 > argument >0

If base>1 then argument > 1

Solving these conditions, we get x$\in (3,\infty )$