Question

对数比较大小，高中数学

以三为底四的对数 以五为底六的对数 试比较大小
请给出具体方法及步骤

Answer 1

∵log4 5/log3 4=log4 5*log4 3<[(log4 5+log4 3)/2]^2=[(log4 15)/2]^2<[(log4 16)/2]^2=1
∴log4 5<log3 4
又∵log5 6/log4 5 =log5 6*log5 4<[(log5 6+log5 4)/2]^2=[(log5 24)/2]^2<[(log5 25)/2]^2=1
∴log5 6<log4 5
由传递性：有log5 6<log3 4

Answer 2

∵log4 5/log3 4=log4 5*log4 3<[(log4 5+log4 3)/2]^2=[(log4 15)/2]^2<[(log4 16)/2]^2=1

∴log4 5<log3 4

又∵log5 6/log4 5 =log5 6*log5 4<[(log5 6+log5 4)/2]^2=[(log5 24)/2]^2<[(log5 25)/2]^2=1

∴log5 6<log4 5

∴有log5 6<log3 4

Answer 3

log3 4=lg4/lg3
log5 6=lg6/lg5
即loga b=logc b/logc a
log3 4>log5 6