Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to at least 4 decimal places. \[ 1026=13^{t}+9 \] There is no solution, \{\} . The exact solution set is $\left\{\frac{\ln 1017}{\ln 13}\right\}$. \[ t \approx \square \] \begin{tabular}{ccc} $\square \ln \square$ & $\square \log \square$ & $\square \log _{a} \square$ \\ $\frac{\square}{\square}$ & $\sqrt[\square]{\square}$ & $\square^{\square}$ \\ $x$ & 5 \end{tabular}

Step 1 ：The given equation is \(1026 = 13^t + 9\).

Step 2 ：To solve for \(t\), we first need to isolate the term with \(t\) on one side of the equation. We can do this by subtracting 9 from both sides of the equation. This gives us \(1017 = 13^t\).

Step 3 ：To solve for \(t\), we can take the natural logarithm of both sides of the equation. This gives us \(\ln(1017) = t \cdot \ln(13)\).

Step 4 ：Finally, we can solve for \(t\) by dividing both sides of the equation by \(\ln(13)\). This gives us \(t = \frac{\ln(1017)}{\ln(13)}\).

Step 5 ：We can calculate this value to get the approximate solution for \(t\).

Step 6 ：The approximate solution for \(t\) is \(\boxed{2.6997}\).