Respected tutor can you please help me to solve this question it is extremely tought, and I am stuckd in it, If you can solve this for me i will definetely give you best rating, just please help me to solve this ASAP with true and proper solution.

(a) Show that the function f : R² B_1/2(0) := {x R² : x₂ 1/2}R defined as f(x) = ln|x| satisfies f L4(B_1/2(0)); here ₂ denotes the standard Euclidean norm. Hint: Exploit that f is rotationally symmetric and use without proof that for 0 < r 1/2 we have ln(1/r) r^1/5.

(b) Let g : [0; 1] [3; 5] be defined as g(x) = {5 if x [0; 1] Q,

3 else. Calculate g_L([0;1]).