Natural Log and Exponential

  • #1

Homework Statement


Trying to solve for K:

ln(1-4k)=-6k


Homework Equations





The Attempt at a Solution


I know that need to take the e of both side, to get 1-4k=e^-6k, but I cannot remember any properties of e to allow me to remove the k from the exponent. Any tips is appreciated.
 

Answers and Replies

  • #2
24
0

Homework Statement


Trying to solve for K:

ln(1-4k)=-6k


Homework Equations





The Attempt at a Solution


I know that need to take the e of both side, to get 1-4k=e^-6k, but I cannot remember any properties of e to allow me to remove the k from the exponent. Any tips is appreciated.

Clearly, [tex]k=0[/tex] is a solution.
to find the another solution you need to use an advanced topic:
http://mathworld.wolfram.com/LambertW-Function.html
 
  • #4
vela
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You have to solve it numerically. You can't solve for k algebraically.

You can visualize the solutions by plotting the functions y=1-4k and y=e^-6k and seeing where they intersect.
 
  • #5
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