How do I solve for K in ln(1-4k) = -6k?

[CursedAntagonis]

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.

 

[Sweet_GirL]

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, $$k=0$$ is a solution.
to find the another solution you need to use an advanced topic:
http://mathworld.wolfram.com/LambertW-Function.html

 

[CursedAntagonis]

Clearly, $$k=0$$ is a solution.
to find the another solution you need to use an advanced topic:
http://mathworld.wolfram.com/LambertW-Function.html

the answer is actually 0.1457 m/s.

 

[vela]

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.

 

[Sweet_GirL]

the answer is actually 0.1457 m/s.

m/s??