If logb2 = r and logb3 = s, then express logb9 square root of 2 in terms of r and s. The correct answer is 2s + 1/2 r but how is the answer that?

r
= logb (2)
= logb (sqrt(2))^2
= 2*logb (sqrt(2))

Thus, logb (sqrt(2)) = r/2

logb 9*(sqrt(2))
= logb 3*3*(sqrt(2))
= logb (3) + logb (3) + logb (sqrt(2))
= s + s + r/2
= 2s + r/2

Note that:
1) log a^b = b*log a for a > 0
2) log a*b = log a + log b for a,b > 0