log2(3)=1+log2(3/2)
log3(4)=1+log3(4/3)<1+log2(4/3)<1+log2(3/2)=log2(3)
所以 log2(3)>log3(4)
如果学过基本不等式
log2(3)>0
log3(4)>0
log2(3)/log3(4)=lg3/lg2/(lg4/lg3)=lg²3/(lg2lg4)
lg2lg4<[(lg2+lg4)/2]²=[(lg8)/2]²<[lg9/2]²=(lg3)²
所以log2(3)/log3(4)>1
所以 log2(3)>log3(4)