Question

Question 3F-2e (http://goo.gl/zTaHE)
Answer http://goo.gl/jFoZc

In the answer to this question, how do we go from -e^-y=x+c
to
y=-ln(4-x)

I understand how c is found, but not how c and x become switched.

Answer 1

-e^-y=x+c
to get rid of the -e^-y they do ln raised to that whole part
ln^-e^-y
the ln and -e cancel (theres a property or something)
so that leaves you -y
and you have to do ln to both sides

-y=ln(x+c)
divide by -1
y=-ln(-x+c)
and then they found the constant is 4
so y=-ln(-x+4)

Answer 2

http://www.rapidtables.com/math/algebra/Ln.htm
Ln as inverse function of exponential function

The natural logarithm function ln(x) is the inverse function of the exponential function ex.

For x>0,

e^ln(x) = x

Or

ln^(e^x) = x

Answer 3

@jackellyn Thank you for your answer. why would would the x change signs as well when you apply
\[-y=\ln(x+4)\] *(-1)
The Algebra doesn't make sense to me there.

Answer 4

You have to multiply the entire right side by -1 to get rid of it from the y
the only reason 4 doesn't change is because its a constant.

Answer 5

even if it is in a parenthesis it still changed

Answer 6

hmm i see
one last question. y=-ln(-x+4) and y=-ln(4-x) are identical here right? (sorry for the additional question)

Answer 7

Yeah they're the same thing
the x is negative in both and the 4 is positive

Answer 8

Alright, thank you very much for your time :)

Answer 9

No problem! :)

Answer 10

That rule comes up a lot in D.E. so make sure you know it