已知x=log底数为(2a)对数为(a),y=log底数为(3a)对数为(2a),求证;2^(1-XY)=3^(y-xy)

问题描述:

已知x=log底数为(2a)对数为(a),y=log底数为(3a)对数为(2a),求证;2^(1-XY)=3^(y-xy)

首先根据(2a)^x=a,log3a2a=y得到2^x=a^(1-x),3^y=2*a^(1-y)2^(1-xy) / 3^(y-xy)=[2/2^(xy)]/[3^(y(1-y))]={2/a^[(1-x)y}/[2*a^(1-y)]^(1-x)=2/{a^(y-xy)*[2*a^(1-y)]^((1-x)=2^x/a^(1-x)=2^x/2^x=1即2^(1-xy) / 3^(y...