# Homework Help: 5e^(7x) = 7e^(10x) ?

1. Sep 14, 2011

### IntegrateMe

5e^(7x) = 7e^(10x) ??

7x ln(5e) = 10x ln(7e)

7x * (ln5 + ln e) = 10x * (ln7 + ln e)

7x * (ln5) = 10x * (ln7)

Now I have nowhere to go. What am I doing wrong?

2. Sep 14, 2011

### Dick

Re: 5e^(7x) = 7e^(10x) ??

5e^(7x) probably means 5*(e^(7x)) not (5e)^(7x) as you are treating it.

3. Sep 14, 2011

### IntegrateMe

Re: 5e^(7x) = 7e^(10x) ??

How does that make a difference?

4. Sep 14, 2011

### Dick

Re: 5e^(7x) = 7e^(10x) ??

All the difference in the world. Try it.

5. Sep 14, 2011

### IntegrateMe

Re: 5e^(7x) = 7e^(10x) ??

5*7x ln e = 7 * 10 ln e

35x = 70x?

This doesn't seem right. Can you please explain how I would start this? Is the 5 included in the natural log?

6. Sep 14, 2011

### Dick

Re: 5e^(7x) = 7e^(10x) ??

ln(5*e^(7x))=ln(5)+ln(e^(7x)). It's looking different already, isn't it? Not the same as ln((5e)^(7x))=7x*ln(5e).

7. Sep 14, 2011

### IntegrateMe

Re: 5e^(7x) = 7e^(10x) ??

Thank you!