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# Interesting problem... degree level maybe?! c3 homework :S e^2x = 10 watch

1. e^(2x) = 10x

how do you solve

homework says, find exact solutions..
i have found one solution using iteration but can't find the other (there are 2..)

how do you find the exact solutions?
2. you are going with this the wrong way, by exact, they mean as a surd, or a fraction, you use ln function in this
3. (Original post by desertwarrior)
e^(2x) = 10x

how do you solve

homework says, find exact solutions..
i have found one solution using iteration but can't find the other (there are 2..)

how do you find the exact solutions?
The title says and your post says Which is correct?
4. (Original post by steve2005)
The title says and your post says Which is correct?
sorry!!

it's

e^(2x) = 10x
5. I don't think there are any exact solutions.

If you're really interested, look up the Lambert W-function.
6. (Original post by DFranklin)
I don't think there are any exact solutions.

If you're really interested, look up the Lambert W-function.
I think that's what wolfram alpha used.. thanks

is there any way to use iteration to find the 2nd solution?
7. (Original post by desertwarrior)
e^(2x) = 10x

how do you solve

homework says, find exact solutions..
i have found one solution using iteration but can't find the other (there are 2..)

how do you find the exact solutions?
Since you are asked for EXACT solutions I think there is an error in the question.
8. if it = 10 it would be easy, just use natural logs.

But 10x seems much harder than C3?
9. (Original post by mfc20)
if it = 10 it would be easy, just use natural logs.

But 10x seems much harder than C3?
yea, weird o.0 use ln on both sides....
10. Ok, you seem to have a misconception that an answer that is accurate to a large number of decimal places is exact. It isn't.

Try both with
11. (Original post by Mr M)
Ok, you seem to have a misconception that an answer that is accurate to a large number of decimal places is exact. It isn't.

Try both with
Ah thanks Mr M!!! That's what i've been working on, but I get one solution converging to 1.2713.........
From the shape of the y=e^2x and y=10x graphs I would assume that there surely should be 2 solutions.. but iteration can only find one from my understanding..

am I forgetting something,
P.s. repped you thanks
12. (Original post by desertwarrior)
Ah thanks Mr M!!! That's what i've been working on, but I get one solution converging to 1.2713.........
From the shape of the y=e^2x and y=10x graphs I would assume that there surely should be 2 solutions.. but iteration can only find one from my understanding..

am I forgetting something,
P.s. repped you thanks
You said the question required EXACT solutions. So iteration will not give the required solution.
13. (Original post by steve2005)
You said the question required EXACT solutions. So iteration will not give the required solution.
yeah but still better than nothing right?
do you know how to find the other solution?
14. How about substitution?
let
so
therefore
use that to find
15. I agree with

I did it by differentiating both sides w.r.t x and it becomes simple to solve. However, the graphical idea of there being two solutions seems quite completing.

I might have to get MatLab out.

EDIT: How does the substitution work?
16. (Original post by ollimollimoll)
let
so
therefore
use that to find
it needs a u after the 5, e^u = 5u
17. (Original post by desertwarrior)
yeah but still better than nothing right?
do you know how to find the other solution?
This is not exact, obviously

18. (Original post by Henerz)

EDIT: How does the substitution work?
Good old substitution:
replace 2x with u, and you can work it out easily. Then, afterwards when solved with u, put 2x back in. Simple

EDIT:that doesn't work, sorry
19. (Original post by Monochrome)
it needs a u after the 5, e^u = 5u
does it?

Ah! you are right. oh well, I tried...
20. (Original post by ollimollimoll)
Good old substitution:
replace 2x with u, and you can work it out easily. Then, afterwards when solved with u, put 2x back in. Simple
i think that is wrong

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