Ok, I was getting all my answers right until I stumbled on this one:

5e^0.2x=7

This is what I was doing:
5e^0.2x=7
5lne^0.2x=ln7
5*0.2x=ln7
0.2x=(ln7/5)
???

The answer is 5ln(7/5) but i do not know how they derived to this. Thank you so much!

1 answer

What you have so far is correct.
you would end up with
x = ln(7/5)/.2 which is the same as their answer.
You just have a different form.

notice you are dividing by .2 or 1/5
and isn't division by 1/5 the same as multiplying by 5?
there you go!
ln(7/5)/.2 = 5ln(7/5)