Problem
Solve the equation, Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. \[ 6^{x}=52 \] There is no solution, \{\}. The exact solution set is $\{[\}$. \[ x \approx \square \] \begin{tabular}{ccc} \hline $\ln \square$ & $\square \log \square$ & $\square^{\log a} a$ \\ $\frac{\square}{\square}$ & $\sqrt[g]{\square}$ & $\square^{\square}$ \\ $\times$ & 5 \end{tabular}
Solution
Step 1 ：The given equation is \(6^{x}=52\).
Step 2 ：We can convert this equation into logarithmic form using the formula \(x = \log_b(a)\).
Step 3 ：Applying this formula, we get \(x = \frac{\ln(52)}{\ln(6)}\).
Step 4 ：Calculating the value of \(x\), we get \(x \approx 2.2052\).
Step 5 ：\(\boxed{\text{The exact solution set is } \{x | x = \frac{\ln(52)}{\ln(6)}\}. \text{The approximate solution is } x \approx 2.2052}\)
