求下列各式中 $x$ 的值.

(1) $\log _{5}\left(\log _{3} x\right)=0$;

(2) $\log _{3}(\lg x)=1$;

(3) $\ln \left(\log _{2}(\lg x)\right)=0$.
【解】 (1) $\because \log _{5}\left(\log _{3} x\right)=\log _{5} 1, \therefore \log _{3} x=1, \therefore x=3$.

(2) $\because \log _{3}(\lg x)=1, \quad \therefore \lg x=3, \quad \therefore x=10^{3}=1000$.

(3) $\because \ln \left(\log _{2}(\lg x)\right)=0, \quad \therefore \log _{2}(\lg x)=1$,

$\therefore \lg x=2, \quad \therefore x=10^{2}=100$.