Question

solve: ( 1/(e^x) ) = 5

Answer 1

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

Answer 2

\[\frac{1}{e^x}=5\]\[1=5*e^x\]\[\frac{1}{5}=e^x\]

Answer 3

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)

Answer 4

from there you simply natural log both sides.

Answer 5

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

Answer 6

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

Answer 7

You understand?

Answer 8

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

Answer 9

haha so many answers

Answer 10

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

Answer 11

okay thank you. that makes sense!

Answer 12

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.