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)
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![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)](/uploads/image/z/8946202-58-2.jpg?t=%E5%B7%B2%E7%9F%A5x%3Dlog%E5%BA%95%E6%95%B0%E4%B8%BA%EF%BC%882a%EF%BC%89%E5%AF%B9%E6%95%B0%E4%B8%BA%EF%BC%88a%EF%BC%89%2Cy%3Dlog%E5%BA%95%E6%95%B0%E4%B8%BA%EF%BC%883a%EF%BC%89%E5%AF%B9%E6%95%B0%E4%B8%BA%EF%BC%882a%EF%BC%89%2C%E6%B1%82%E8%AF%81%EF%BC%9B2%5E%281-XY%29%3D3%5E%EF%BC%88y-xy%EF%BC%89)
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)
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)
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-xy)=1,所以2^(1-xy)=3^(y-xy).