Question

计算下列公式 (1）（2lg2+lg3)/(1+1/2lg0.36+1/3lg8) (2) lg5^2+2/3lg8+lg5*lg20+(lg2)^2

Answer 1

(1)解：
原式=lg12/(lg10+lg0.6+lg3)
=lg12/lg18
=log18(12)

(2)解：
原式=2lg5+2lg2+lg5*(2lg2+lg5)+(lg2)²
=(lg5)²+2lg5lg2+(lg2)²+2(lg5+lg2)
=(lg5+lg2)²+2lg10
=(lg10)²+2
=1+2
=3

Answer 2

1.(2lg2+lg3)/(1+0.5lg0.36+1/3lg8)
=(lg4+lg3)/(1+lg√0.36 +lg(2^3)^(1/3))
=lg12/(1+lg0.6+lg2)
=lg12/(lg10+lg0.6+lg2)
=lg12/lg(10*0.6*2)
=lg12/lg12
=1