# Solve the following equationWatch

#1
e^x = 3(x^2)
0
10 years ago
#2
(Original post by blackdragonthegreat)
e^x = 3(x^2)
There are three roots between -1,0 and 0,1 and 3,4 but I doubt any of them can be found exactly and you're going to have to use numerical methods.
0
10 years ago
#3
You can do something with the Lambert-W function if you really want...
0
10 years ago
#4
e^x = 3(x^2) and the answer is,.....

{x = -2*LambertW(-(1/6)*sqrt(3)*ln(e))/ln(e)}, {x = -2*LambertW((1/6)*sqrt(3)*ln(e))/ln(e)}

Wow...!
0
10 years ago
#5
Can simplify that a bit I think... (ln e???) Not entirely sure where the 3rd root is disappearing though, but the LambertW func is multivalued for suitably negative x.
0
#6
(Original post by doddy3)
e^x = 3(x^2) and the answer is,.....

{x = -2*LambertW(-(1/6)*sqrt(3)*ln(e))/ln(e)}, {x = -2*LambertW((1/6)*sqrt(3)*ln(e))/ln(e)}

Wow...!
i dont see the pont in multiplying by lne then also dividing by it?
0
10 years ago
#7
(Original post by blackdragonthegreat)
i dont see the pont in multiplying by lne then also dividing by it?
Looks like the ln e is an argument to the Lambert-W function.
0
10 years ago
#8

Then...uh... I dunno <_<
0
#9
(Original post by EvenStevens)

Then...uh... I dunno <_<
your manipulation of logarithms is wrong
ln(3.x^2) is
ln3 +2lnx
0
10 years ago
#10
Whoops.. Thanks for that >_<
0
#11
(Original post by EvenStevens)
Whoops.. Thanks for that >_<
thats alright, no probs.
0
10 years ago
#12
Isn't ln3x^2=ln3+2lnx?

I used a graphing calculator for ln(3)= x-2ln(x)
According to it, the answer was 0.91.
0
10 years ago
#13
By plotting e^x and 3x^2 in the same X-Y axis, you get to see the estimates of the would be right answers! otherwise you ll have to rely on LambĀ£t-W function! how did I get it?! Well I used Maple !
0
10 years ago
#14
,

,

,

. Write y = -x/2, then

.

Then (as LambertW is defined as the inverse function of f(y) = ye^y).

0
#15
(Original post by DFranklin)
,

,

,

. Write y = -x/2, then

.

Then (as LambertW is defined as the inverse function of f(y) = ye^y).

how does rt3x go to rt12(x/2)

never mind
0
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