已知log a (xy)==√2,log a (ay)=2 求log a x的值

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已知log a (xy)==√2,log a (ay)=2 求log a x的值

已知log a (xy)==√2,log a (ay)=2 求log a x的值
已知log a (xy)==√2,log a (ay)=2 求log a x的值

已知log a (xy)==√2,log a (ay)=2 求log a x的值
logax+logay=loga(xy)
loga(ay)=1+logay,logay=2-1=1
logax=log a (xy)-log a y=√2-1

a>0,logax十logay=√2,a^2=ay,故y=a,故logax +logaa=√2,所以logax =√2—1

log a (xy)==log a x+log a y=√2
log a (ay)=log a(a)+log a y=1+log a y=2
∴log ay=1
∴log a x=√2-1

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