x+lgx=3

lgx=3-x

Both sides of the equal sign are monotonous, and the picture shows that,

Only one x value matches.

When x= 1, the left side =0 and the right side =2.

Left to right =0 when x=3 > 0.

therefore

The value of x is 1 to 3.

When x takes 2,

Left = lg2

Right = 1

So x takes a value between 2 and 3.

k=2