指数和对数的公式总结
1. 指数基本公式
),,0(R n m a a a a n m n m ∈>⋅=+
),,0(R n m a a
a a n m
n m ∈>=- ),,0()(R n m a a a mn n m ∈>=
),0()(R n a a a ab n n n ∈>=
)1,,,0(>∈>=n N n m a a a n m n m
)1,,,0(11
>∈>==-n N n m a a a a n m n m
n m
2. 对数基本公式
N a N a =log
N a N a =log
N M MN a a a log log )(log +=
N M N
M a a a log log )(log -= )(log log R n M n M a n a ∈=
a
N N b b a log log log = 3. 对数与指数互换
)0,10(log >≠>=⇔=N a a N a b N b a 且
4. 常用变式
1) 基本变形
)0,10(log )()(>≠>=⇔=b a a b x f b a a x f 且 )0)(,10()()(log >≠>=⇔=x f a a a x f b x f b a 且
2) 同底变形
)10)(()()()(≠>=⇔=a a x g x f a a x g x f 且 )10(0)()()(log )(log ≠>>=⇔=a a x g x f x g x f a a 且
