Equations involving logarithms

$\log_{10} (x) = 10^{\log_{10}(3)}\\ \log_{10}\left(\log_{10} (x) \right) = \log_{10}\left(10^{\log_{10}(3)}\right)\\ \log_{10}\left(\log_{10} (x) \right) = \log_{10}(3)\log_{10}(10)\\ \log_{10}\left(\log_{10} (x) \right) = \log_{10}(3)\\ \log_{10}(x) = 3\\ x=10^3 = \boxed{1000}$

$\log_{10}(x)=10^{\log_{10}(3)}$ or $\log_{10}(x)=3$ or $x=10^3=\boxed{1000}$ .

$\begin{aligned} \log_{10}(x) = 10^{\log_{10}(3)} &\Rightarrow \log_{10}(x) = \log_{10}\left(10^{10^{\log_{10}(3)}}\right) \\&\Rightarrow x = 10^3 \\&\Rightarrow x = 1000 \space \square \end{aligned}$

$\LARGE \text{ADIOS!!!}$