Question

f(x)=2(ln x)^2 - 3 ln(x) evaluate at x=2e

after plugging in everything I have reached this point...

2(ln2+1)^2-3(ln2+1)

if I foil out (ln2+1)^2 I get 2(ln2) + ln 2 + ln 2 +1. Not sure what to do from here. Do I combine it to 2ln(2) + 2ln(2)+1??? Help please!

Answer 1

here f(x)=2(lnx)^2-3lnx
putting x=2e,
f(2e)=2[ln(2e)]^2-3ln(2e)=2[ln2+1]^2-3[ln2+1]=2[(ln2)^2+2ln2+1]-3ln2-3
=2(ln2)^2+ln2-1
put ln2=0.693
f(2e)=0.65349