I need help proving these problems

1. logx + logy = log(xy) 2. loglab ] = log a + (log b) (log c) 3. o(x) = o(x) x (1 -o(x)) where o(x) = 1/(1 + e-x) 4. The distance between the point (x1, y1) and line ax + by + c is (axl + by1 + c)/Va + 62 logx = - 5. ax 6. p(a | b) = p(a, b)/p(b) 7. p(x | y, z) = p(x | y)p(x | z) 8. C(n, k) = C(n - 1, k - 1) + C(n - 1, k), where C(n, k) is the number of ways of choosing k objects from n 9. llau + v/12 = 02 (lull" + |lull", where II.|| denotes Euclidean norm, a is a scalar and u and v are vectors 10. JuTv > |lull x |lull, where |.| denotes absolute value and u v is the dot product of u and v 11. Soda exp[-(7/2)x2] = V2