Question

设log2(5)=x,log5(3)=y,试用x,y表示log24(20)

Answer 1

x=log2(5)=lg5/lg2

y=log5(3)=lg3/lg5

log24(20)=lg(20)/lg(24)=lg(4×5)/lg(8×3)=(lg4+lg5)/(lg8+lg3)

=(2lg2+lg5)/(3lg2+lg3)

=(2 +lg5/lg2)/(3 +lg3/lg2)

=(2+lg5/lg2)/[3+(lg3/lg5)(lg5/lg2)]

=(x+2)/(xy+3)