This condition is best solved by splitting the situation according to
the sign of x − 2, note that it cannot be zero (otherwise
the whole expression would be zero, which we do not want).
If x − 2 < 0, then the condition
ln(x) < 0 leads to
x < 1. The conditions
x − 2 < 0 and
x < 1 now have to be intersected.
If x − 2 > 0, then the condition
ln(x) > 0 leads to
x > 1. The conditions
x − 2 > 0 and
x > 1 now have to be intersected.
Take union of these possibilities.