Exponentials & Logarithms Watch

OllyThePhilosopher
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#1
Report Thread starter 10 years ago
#1
I'm trying to solve:

1+e^(2x+1)=3-e^x

I've got as far as:

e.e^(2x)+e^x-2=0

But I can't factorise it. Any help would be appreciated. Thanks x
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RichE
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#2
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(Original post by OllyThePhilosopher)
I'm trying to solve:

1+e^(2x+1)=3-e^x

I've got as far as:

e.e^(2x)+e^x-2=0

But I can't factorise it. Any help would be appreciated. Thanks x
It might not be easily factorisable - if you can't use the quadratic formula
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aster100
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#3
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#3
(Original post by nuodai)
By the looks of it you need to take logarithms of both sides:

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1 + e^(2x+1) = 3 - e^x
ln 1 + (2x+1) = ln 3 + x
x = ln 3 - 1


Actually I think I'm wrong here, but yeah.
Very very poor.

Use the quadratic formula. You can't factorise that in a simple way. Especially seeing as you have e as a coefficient.
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OllyThePhilosopher
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(Original post by nuodai)
Actually I think I'm wrong here, but yeah.
Lol, yeah you can't log like that. Thanks anyway though.
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nuodai
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#5
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I realised how stupid I was after posting, and I couldn't be bothered to delete it. I might do that now actually, sorry!
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OllyThePhilosopher
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#6
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(Original post by aster100)
Very very poor.

Use the quadratic formula. You can't factorise that in a simple way. Especially seeing as you have e as a coefficient.
I think you're right. Thank you
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wanderlust.xx
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#7
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Quadratic formula. If that fails... Numerical Methods and find the range of the roots... I doubt that'd happen though. >.>;
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