Need help solving for x

Bokan96

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Jul 5, 2019
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I can't figure out how to get rid of the logarithm. There are supposed to be 3 results since it's equation power of 3 right?
(ln x/2 - 2)2 * x = e
Thanks in advance!
 

Subhotosh Khan

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Jun 18, 2007
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I can't figure out how to get rid of the logarithm. There are supposed to be 3 results since it's equation power of 3 right?
(ln x/2 - 2)2 * x = e
Thanks in advance!
Does the given expression look like:

\(\displaystyle \displaystyle{[ln(\frac{x}{2}) - 2]^2 * x \ = \ e}\)
 

Bokan96

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Jul 5, 2019
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Yes, that's it. I don't even know where to begin from.
 

pka

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Jan 29, 2005
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I can't figure out how to get rid of the logarithm. There are supposed to be 3 results since it's equation power of 3 right?
(ln x/2 - 2)2 * x = e
\(\displaystyle {\left[ {\log \left( {\frac{x}{2}} \right) - 2} \right]^2} = {\log ^2}\left( {\frac{x}{2}} \right) - 4\log \left( {\frac{x}{2}} \right) + 4\)
 

Dr.Peterson

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Nov 12, 2017
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I can't figure out how to get rid of the logarithm. There are supposed to be 3 results since it's equation power of 3 right?
(ln x/2 - 2)2 * x = e
Thanks in advance!
This is not a polynomial in x, so it doesn't necessarily have three solutions.

In fact, it is a transcendental equation, with x both inside and outside a logarithm, so it probably can't be solved to give a closed-form expression for x. Numerical methods are probably required. From a graph, it appears to have three solutions, around 0.115, 8.354, and 21.15.
 
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