Question

Evaluate f(x)= 2(ln x)^2 - ln(x) at x=2e So first I plugged in 2e in every x I see. So I get 2(ln(2e))^2- 3ln(2e) Then I know that lne=1 so ln(2e)=ln2+lne or ln(2e)=ln2+1 so I can plug that in where I see ln(2e) so I then get 2(ln2+1)^2 - 3(ln2+1) and now I AM STUCK!

Answer 1

I think if we back up it might make things a little easier.
First factor out a \(\ln x\) from each term.
\[\large f(x)=\ln x(2\ln x-1)\]
Now let's plug in 2e at this point,\[\large f(2e)=\ln(2e)(\ln(2e)-1)\]

Now from here, let's apply your little trick :)\[\large f(2e)=(\ln2+1)(\ln2+1-1)\]\[\large f(2e)=(\ln2+1)\ln2\]



If you don't want to back up like I did, you can simply factor out a (ln2+1) from each term on the step you got to.

After that, I'm not sure if there is any more simplification that can be done.
I think we need to use a calculator from here :D

Answer 2

Thank you for your explanation! I appreciate it a lot. Thing is this answer is not one of the answers available! =( I am not sure what else to do.