Solve the given equation, first approximately by filling in the given table, then to four decimal places by using logarithms. \[ 2^{x}=20 \] Round your answers in the table to three decimal places. \begin{tabular}{|c|c|c|c|c|} \hline$x$ & 4.1 & 4.2 & 4.3 & 4.4 \\ \hline $2^{x}$ & i & i & i & i \\ \hline \end{tabular} Using the table, $x=$ Using logarithms, $x=$ eTextbook and Media

Step 1 ：The problem is asking to solve the equation \(2^{x}=20\) by two methods. First, we need to fill in the table for the values of \(x\) from 4.1 to 4.4 and calculate the corresponding \(2^{x}\) values. Then, we need to solve the equation using logarithms.

Step 2 ：Fill in the table with the calculated values of \(2^{x}\) for each given \(x\). The table values are approximately [17.148, 18.379, 19.698, 21.112] for \(x\) values of 4.1, 4.2, 4.3, and 4.4 respectively.

Step 3 ：From the table, we can see that the value of \(2^{x}\) is getting closer to 20 as \(x\) increases from 4.1 to 4.4. However, none of the values in the table are exactly 20.

Step 4 ：Next, solve the equation using logarithms. The equation \(2^{x}=20\) can be rewritten in logarithmic form as \(x = \log_{2}{20}\).

Step 5 ：Calculate the value of \(x\) using the logarithm formula. The approximate value of \(x\) is 4.3219.

Step 6 ：Final Answer: Using the table, \(x\) is approximately between 4.3 and 4.4. Using logarithms, \(x\) is approximately \(\boxed{4.3219}\).