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)