a的b次方等于b的a次方,b等于9a,求a

Question

a的b次方等于b的a次方,b等于9a,求a

Answer 1

a^b=b^a
blog(3,a)=alog(3,b)
b=9a代人
9alog(3,a)=alog(3,9a)
9alog(3,a)=alog(3,3^2*a)=a(log(3,3^2)+log(3,a))
=a(2+log(3,a))
即 9log(3,a)=2+log(3,a)
8log(3,a)=2
log(3,a)=1/4
a=3^(1/4)
log(3,a)表示3为底数,a为幂的指数
现在够详细了吧