Solve the equation, first approximately by filling in the given table, and then to four decimal places by using logarithms. \[ 10^{x}=2500 \] Round your answers in the table to three decimal places. \begin{tabular}{|c|c|c|c|c|} \hline$x$ & 3.2 & 3.3 & 3.4 & 3.5 \\ \hline $10^{x}$ & 1584.893 & 1995.262 & 2511886 & 3162.278 \\ \hline \end{tabular} Using the table, $x=3.4$. Using logarithms, $x=$

Step 1 ：Solve the equation, first approximately by filling in the given table, and then to four decimal places by using logarithms. The equation is \(10^{x}=2500\). Round your answers in the table to three decimal places.

Step 2 ：Fill in the table: \n\begin{tabular}{|c|c|c|c|c|}\n\hline$x$ & 3.2 & 3.3 & 3.4 & 3.5 \\ \hline $10^{x}$ & 1584.893 & 1995.262 & 2511886 & 3162.278 \\ \hline\n\end{tabular}\nUsing the table, $x=3.4$.

Step 3 ：To solve the equation \(10^{x}=2500\) using logarithms, we can take the logarithm of both sides of the equation. This will allow us to isolate $x$ and solve for it. We can use the property of logarithms that states \(\log_{b}(a^n) = n \cdot \log_{b}(a)\) to simplify the equation.

Step 4 ：Calculate the value of $x$ using logarithms: $x = 3.3979400086720375$

Step 5 ：Final Answer: Using logarithms, $x=\boxed{3.3980}$ when rounded to four decimal places.