中四maths log問題;(20分)急;

1. log x + log 2y = 2
log (2xy) = 2
2xy = 10^2 = 100
xy = 50
y = 50/x

2. log√45
= log [45^(1/2)]
= 1/2 log 45
= 1/2 log (3^2 * 10 / 2)
= 1/2 [log 3^2 + log 10 - log 2]
= 1/2 [2 log 3 + 1 - log 2]
= 1/2 (2b + 1 - a)
= -a/2 + b + 1/2

3. [log (x^3) + log√x] / [2 log(1/x)]
= [log (x^3) + log (x^{1/2})] / [2 log (x^{-1})]
= [3 log x + 1/2 log x] / [-2 log x]
= (3 + 1/2) / (-2)
= -7/4