Find the intermediate quantity by trying that both of them are greater than 1/2.

Less than 3/4

log3(2)>log3(√3)= 1/2

log2(3/2)>log2(√2)= 1/2

log3(2)& lt； log3(3^3/4)=3/4

log2(3/2)& lt； log2(2^3/4)=3/4

Consider using 0.6 or 3/5 as an intermediate quantity.

log3(2)>log3(3^3/5)=0.6

log2(3/2)& lt； log2(2^3/5)=0.6

So log3(2) is very large.