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58问答库 > 高中代数对数中换底公式怎么证明？

高中代数对数中换底公式怎么证明？

2025-04-07 05:13:33

推荐回答（1个）

回答（1）：

设a^b=N…………①
则b=logaN…………②
把②代入①即得对数恒等式：
a^(logaN)=N…………③
把③两边取以m为底的对数得
logaN·logma=logmN
所以
logaN=(logmN)/(logma)

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