## anonymous 4 years ago solve: ( 1/(e^x) ) = 5

1. anonymous

This is tricky one you will have to use natural log.

2. anonymous

$\frac{1}{e^x}=5$$1=5*e^x$$\frac{1}{5}=e^x$

3. zzr0ck3r

1/e^(x) = 5 e^(x) = 1/5 ln(e^(x)) = ln(1/5) x = ln(1/5) = ln(1) - ln(5) = 0 - ln(5) = -ln(5)

4. anonymous

from there you simply natural log both sides.

5. anonymous

$e^{-x}=5$ does this look better? or maybe $e^{x}= \frac{1}{5}$

6. anonymous

The natural log will cancel the e and bring down the x

7. anonymous

You understand?

8. anonymous

so the answer would be ln(1/5) ?

9. anonymous

10. anonymous

Yes that is the answer. You can simplify it however you want. I would just leave it as that.

11. anonymous

okay thank you. that makes sense!

12. zzr0ck3r

notice that 1/5 = 5^(-1) and a property of logs is a*log(b) = log(b^a) so log(1/5) = log(5^(-1)) = -1*log(5) this is the great thing about logs, you can really "play around" with them. notice how i got to the same thing two compelety different ways.