# Thread: Problem in my Calc. homework

1. ## Problem in my Calc. homework

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.

2. Originally Posted by redsoxfan0825
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.
Take logs of both sides:

$\ln{5e^{5t}}=\ln{7e^{4t}}$

Now use the properties of logs to finish up.

3. Properties of logarithms, refresh me on those? The highest math I took in HS was trig and I don't think there's anything like this problem in my notes. If you don't have the time, no big deal I'm sure I'll figure it out. Thanks for the help.

4. $5e^{5t} = 7e^{4t}$

$5e^{5t} - 7e^{4t} = 0$

$e^{4t}(5e^t - 7) = 0$

since $e^{4t} > 0$ for all $t$ ...

$5e^t = 7$

$e^t = \frac{7}{5}$

$t = \ln\left(\frac{7}{5}\right)$

you still need to learn the properties of logs ... you'll need them.