Log Question (No calculator) Please help!

log base 3(log base 8(log base 10(x))) = -1

(log((log((log(x))/(log(10))))/(log(8))))/(log(3)) = -1

log base 3(log base 8(log base 10(x))) = -1

$\small{ \begin{array}{rcl} \log_3{~ \{ \log_8{ [ ~ \log_{10}{ (x) } ~]} ~\}} &=& -1 \qquad | \qquad u = \log_8{ [ ~ \log_{10}{ (x) } ~]}\\ \log_3{ (u) } &=& -1 \\ 3^{ \log_3{ (u) } } &=& 3^{-1} \\ u &=& \frac13 \\ \\ \hline \\ u = \log_8{ [ ~ \log_{10}{ (x) } ~]} &=& \frac13 \qquad | \qquad v = \log_{10}{ (x) }\\ \log_8{ (v) } &=& \frac13 \\ 8^{ \log_8{ (v) } } &=& 8^{\frac13 } \\ v &=& 8^{\frac13 } \\ v &=& 2^{\frac33} \\ v &=& 2 \\ \\ \hline \\ v = \log_{10}{ (x) } &=& 2 \\ 10^{ \log_{10}{(x)} } &=& 10^{ 2} \\ \mathbf{x} & \mathbf{=} & \mathbf{100} \end{array} }$