You have the following equation:
[tex]e^{5t}=261[/tex]
In order to solve for t, use the following property:
[tex]\ln e^a=a[/tex]
Then, apply ln both sides of the given equation, and solve for t:
[tex]\begin{gathered} \ln e^{5t}=\ln (261) \\ 5t=5.564 \\ t=\frac{5.564}{5} \\ t=1.1129\approx1.113 \end{gathered}[/tex]
Hence, the value of t is t = 1.113
