Question

Solve for x
3 = 2 +5e^-4x

Answer 1

\[3 = 2+5e ^{-4x}\]

Answer 2

How about you move that 2 over to the other side

Answer 3

\[1 =5e ^{-4x}\]

Answer 4

Then, divide over that 5:
\[1/5 = 5e ^{-4x}/5\]

Answer 5

So then we end up getting:
\[\frac{1}{5} = e^{-4x}\]

Answer 6

Now, we want to get rid of that "e". How can we do so?

Answer 7

What do we know "cancels" out the base "e"?

Answer 8

Is it using ln?

Answer 9

Yes! Good job

Answer 10

So now, we ln both sides:
\[\ln(\frac{1}{5}) = \ln(e^{-4x})\]

Answer 11

So what happens to the ln(e..) expression?

Answer 12

They essentially "cancel" each other out, leaving you with ____

Answer 13

Understand? Do you know how to carry on from here?

Answer 14

I divide it by 4?

Answer 15

Yes, you should end up getting (for the right hand side), a -4x remaining after you "cancel" out the ln and "e".

Answer 16

No, you divide by NEGATIVE 4

Answer 17

And then you should be done, unless you want an estimate. The value:
\[\frac{\ln(\frac{1}{5})}{-4}\]

is an exact value.

Answer 18

So if you want the exact answer, that would be it.

Answer 19

Wow, thank you. I keep forgetting how and when to use the formulas. Thanks again!

Answer 20

So the idea of these types of problems is that you:
1) want to get rid of the e's

Answer 21

This is what you should do when experiencing an equation to solve for x: ask yourself, what is the problem, and how can I get rid of it?

Answer 22

Your welcome.

Answer 23

Your one of the best people explaining equations on here! Thanks for helping me out and giving me a tip! :)

Answer 24

I am sure there are others too that are far more knowledgable in this board than me, wait till they help you out. :)