log2(3)=a

lg3/lg2=a

log6( 16)= LG 16/lg6 = 4lg 2/(lg2+lg3)= 4/( 1+lg3/lg2)= 4/( 1+ 1/a)= 4a/(a+ 1)

2. let log2(3)=a, log3(5)=b, and use a and b to represent log 15(20).

lg3/lg2=a，lg5/lg3=b

log 15(20)=(lg4+lg5)/(lg3+lg5)=(2lg 2/lg3+lg5/lg3)/( 1+lg5/lg3)=(2/a+b)/( 1+b)=(2+ab)/(a+ab)