2^log5 3 与3^log5 2 比大小
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2^log53与3^log52比大小2^log53与3^log52比大小2^log53与3^log52比大小令a=2^log53b=3^log52lga=log5(3)lg2=(lg3/lg5)*lg
2^log5 3 与3^log5 2 比大小
2^log5 3 与3^log5 2 比大小
2^log5 3 与3^log5 2 比大小
令a=2^log5 3
b=3^log5 2
lga=log5(3)lg2=(lg3/lg5)*lg2=(lg2lg3)/lg5
lgb=log5(2)lg3=(lg2/lg5)*lg3=(lg2lg3)/lg5
lga=lgb
所以a=b
所以2^log5 3=3^log5 2
换底,换底会吗?对数都换成以2底和以三为敌的,一化简就行了
两边同时取以5为底的对数,有
㏒5 2^log5 3=log5 3㏒5 2
㏒5 3^log5 2 =log5 2㏒5 3
∴㏒5 2^log5 3=㏒5 3^log5 2
∴2^log5 3 =3^log5 2
反正这2个不相等
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