Need help solving for x

[Bokan96]

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!

 

[Deleted member 4993]

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]

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

 

[pka]

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]

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.