Question

已知logax+3logxa-logxy=3(大于1),若y的最小值是8求a和x

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

x=2^6

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Thanks,

Yoga