Solve for t using natural logarithms
5e^5t=7e^4t
I tried doing it 3 or 4 times, but I don't seem to be making much progress. The answer is rounded to 3 places.
$\displaystyle 5e^{5t} = 7e^{4t}$
$\displaystyle 5e^{5t} - 7e^{4t} = 0$
$\displaystyle e^{4t}(5e^t - 7) = 0$
since $\displaystyle e^{4t} > 0$ for all $\displaystyle t$ ...
$\displaystyle 5e^t = 7$
$\displaystyle e^t = \frac{7}{5}$
$\displaystyle t = \ln\left(\frac{7}{5}\right)$
you still need to learn the properties of logs ... you'll need them.