Answer
\[\boxed{\begin{array}{*{20}{c}}
x&{\frac{{{{\left( {\ln x} \right)}^4}}}{x}} \\
{10}&{2.8110} \\
{{{10}^2}}&{4.4976} \\
{{{10}^4}}&{0.7196} \\
{{{10}^6}}&{0.03643} \\
{{{10}^8}}&{0.001151} \\
{{{10}^{10}}}&{0.00002811}
\end{array}}\]
Work Step by Step
$$\eqalign{
& \frac{{{{\left( {\ln x} \right)}^4}}}{x} \cr
& {\text{Completing the table of values:}} \cr
& x = 10 \to \frac{{{{\left( {\ln 10} \right)}^4}}}{{10}} \approx \frac{{28.1101}}{{10}} \approx 2.8110 \cr
& x = {10^2} \to \frac{{{{\left( {\ln {{10}^2}} \right)}^4}}}{{100}} \approx \frac{{449.7619}}{{100}} \approx 4.4976 \cr
& x = {10^4} \to \frac{{{{\left( {\ln {{10}^4}} \right)}^4}}}{{{{10}^4}}} \approx \frac{{7196.1916}}{{10000}} \approx 0.7196 \cr
& x = {10^6} \to \frac{{{{\left( {\ln {{10}^6}} \right)}^4}}}{{{{10}^6}}} \approx \frac{{36430.7201}}{{1000000}} \approx 0.03643 \cr
& x = {10^8} \to \frac{{{{\left( {\ln {{10}^8}} \right)}^4}}}{{{{10}^8}}} \approx \frac{{115139}}{{100000000}} \approx 0.001151 \cr
& x = {10^{10}} \to \frac{{{{\left( {\ln {{10}^{10}}} \right)}^4}}}{{{{10}^{10}}}} \approx \frac{{281101}}{{10000000000}} \approx 0.00002811 \cr} $$
\[\boxed{\begin{array}{*{20}{c}}
x&{\frac{{{{\left( {\ln x} \right)}^4}}}{x}} \\
{10}&{2.8110} \\
{{{10}^2}}&{4.4976} \\
{{{10}^4}}&{0.7196} \\
{{{10}^6}}&{0.03643} \\
{{{10}^8}}&{0.001151} \\
{{{10}^{10}}}&{0.00002811}
\end{array}}\]
