anonymous
  • anonymous
solve: ( 1/(e^x) ) = 5
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
This is tricky one you will have to use natural log.
anonymous
  • anonymous
\[\frac{1}{e^x}=5\]\[1=5*e^x\]\[\frac{1}{5}=e^x\]
zzr0ck3r
  • 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)

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anonymous
  • anonymous
from there you simply natural log both sides.
anonymous
  • anonymous
\[e^{-x}=5\] does this look better? or maybe \[e^{x}= \frac{1}{5}\]
anonymous
  • anonymous
The natural log will cancel the e and bring down the x
anonymous
  • anonymous
You understand?
anonymous
  • anonymous
so the answer would be ln(1/5) ?
lgbasallote
  • lgbasallote
haha so many answers
anonymous
  • anonymous
Yes that is the answer. You can simplify it however you want. I would just leave it as that.
anonymous
  • anonymous
okay thank you. that makes sense!
zzr0ck3r
  • 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.

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