25: The conditions give (in the same order):
- Since always
2 ≤ 3+sin(x) ≤ 4,
the first condition is always true.
- This condition is true for all x, see the estimate above.
- This condition on base of logarithm is
x > 0 and
x ≠ 1.
This restriction can be also found using the formula
log x(2) = ln(2)/ln(x).
Now intersect these conditions.
Answer