Calculus problem which requires me to isolate X

[paiway]

I'm solving a calculus problem which requires me to equate both equations, but I can't isolate X:

√x = e^-3x

What I've got so far is:

ln√x = ln e^-3x

ln√x = -3x

1/2 ln x = -3x

ln x = -6x ... but from here I can't continue, please help

 

[praharmitra]

you mean you want to solve for x right?? well, i don't think that can be done in terms of standard functions.

 

[sutupidmath]

Yeah, like said, i can only show that a sol, to this eq exists, but i don't believe there is a solution algebraically. YOu can only solve it numerically.

 

[Gib Z]

I have quite a remarkable exact solution -

The GibZ Constant - G​

where G is defined to be the unique solution to the equation $log_e x + 6x = 0$ lol.

 

[th3plan]

well if you got to here , heh , just a thought

ln x = -6x

take e to both sides
and get x=e^-6x

:D

 

[sutupidmath]

well if you got to here , heh , just a thought

ln x = -6x

take e to both sides
and get x=e^-6x

:D

...and...end up with exactly what you started with...lol...