Question

f(x)=3的x-2的次方,f(log9的x次方）=1/2,

Answer 1

令 t=log9(x) ,则 x=9^t ,两边取以3为底的对数,则

log3(x)=log3(9^t)=t*log3(9)=2t ,

由已知得 f(t)=3^(t-2)=1/2 ,

所以,两边取以3为底的对数,则

t-2=log3(1/2),

t=2+log3(1/2)=log3(9)+log3(1/2)=log3(9/2) ,

由此得 log3(x)=2t=2log3(9/2)=log3[(9/2)^2]=log3(81/4) ,

所以 x=81/4 .