Chapter 5 - Logarithmic Functions - 5.1 Logarithms and Their Properties - Exercises and Problems for Section 5.1 - Skill Refresher - Page 193: S7

$t=\frac{14}{9}$

Using the fact that $\sqrt{a}=a^\frac{1}{2}$ and $(a^m)^n=a^{mn}$, the equation becomes $$e^\frac{9t}{2}=e^7$$ This implies that $\frac{9t}{2}=7$. Multiply both sides by $\frac{2}{9}$ to cancel the fractional coefficients and get $$t=7 \cdot \frac{2}{9}=\frac{14}{9}$$