求证明 a^(log(c)(b))=b(log(c)(a))

求证明 a^(log(c)(b))=b(log(c)(a))
求证明 a^(log(c)(b))=b(log(c)(a))

求证明 a^(log(c)(b))=b(log(c)(a))
证明：a^(log(c)(b))=a^[log(a)(b)/log(a)(c)].用换底公式换成a为底
=[a^(log(a)(b))]^[1/log(a)(c)].利用指数的性质
=[b]^[1/log(a)(c)].利用对数恒等式a^(log(a)(b))=b
=b^(log(c)(a)).利用对数的性质log(c)(a)=1/log(a)(c)