f(x)=(Ln x)^{2}- 3Ln x
x=2e
----------------------------------------------------
(ln(2e))^{2}-3ln(2e)
2ln2e-3ln(2e)
im stuck :| logs and natural logs are the most confusing thing ever
$\ln(2e)^2 = 2\ln(2e)$ is not correct.
What is correct is
$\ln((2e)^2)=2\ln(2e)$
Looking at your problem.
$f(x)=(\ln(x))^2-3\ln(x)$
$f(2e)=(\ln(2e))^2 - 3\ln(2e)$
this is actually in fairly simple form. You could further do the following
$u=\ln(2e)$
$f(2e)=u^2-3u = (u-1.5)^2-2.25 = (\ln(2e)-1.5)^2-2.25$
I think you read my answer wrong hahaa, could you also go step by step?
but i was given these answer choices:
1. f(2e) = 3(ln 2)2+ ln 2 + 2
2. f(2e) = 3(ln 2)2+5 ln 2 + 4
3. f(2e) = (ln 2)2− ln 2 − 2
4. f(2e) = (ln 2)2+ ln 2 + 2
5. f(2e) = 3(ln 2)2− ln 2 − 2
6. f(2e) = (ln 2)2−5 ln 2 − 4
7. f(2e) = 3(ln 2)2−5 ln 2 − 4
8. f(2e) = (ln 2)2+5 ln 2 + 4