log25﹙3﹚=a,log25﹙4﹚=b,求log5﹙72﹚

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/09/13 11:25:08

log25﹙3﹚=a,log25﹙4﹚=b,求log5﹙72﹚
log1/27(1/7)=a,log1/3(1/5)=b,求log81(175)

∵log25﹙3﹚=log(5²)3=1/2log(5)3=a
∴log(5)=2a
∵log25﹙4﹚=log(5²)4=1/2log(5)4=b,
∴log(5)4=2b
∴log5﹙72﹚=log(5)(4×18)
=log(5)4+log(5)(2×3²)
=2b+1/2log(5)4+2log(5)3
=2b+b+2*2a
=4a+3b
2
log1/27(1/7)=log(3³)7==1/3log(3)7=a,
∴log₃7=3a
log1/3(1/5)=log₃5=b,
log81(175)
=log₃175/log₃81
=1/4*log₃(7×5²)
=1/4*[log₃7+2log₃5]
=(3a+2b)/4

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