Recurrence Question involving logarithm

Question

Can anyone please solve this recurrence

$$T(n)=T(3\sqrt n)+\log n.$$

It came in my paper. I want to know whether the following answer is right or wrong:

My answer: $T(n)=\log^3 n.$

Answer 1

For $n=9$ the recurrence $T(n)=T(3\sqrt n)+\lg n$ gives

$T(9)=T(9)+\lg 9$,

hence $\lg9=0$ ??

Something wents wrong ...