Question

已知a（a>0,且a不等于1)变数x,y之间有logaX+3logxa-logxY=3若y有最小值8求a的值

Answer 1

logax+3logxa-logxy=3 logax=3/logax-3=logay/logax IF logax=t logay=g(x) g(x)=t^2-3t+3 a>1 y min=8 => g(x)min g(x)=ax^2+bx+c a>0 x=-b/2a y=4ac-b^2/4a => x=3/2 y=3/4 loga8=g(x)=3/4=>a^(3/4)=8=>a^(3/4*4/3)=8^(4/3)=>a=2^4 logax=t=3/2=>log2^4 x=3/2=>2^[4*(3/2)]=x=>x=2^6 a=2^4