Question

Evaluate the following expressions. Your answers must be exact and in simplest form.
lne^-11=?
e^(ln4)=?
e^(lnsqrt(3))=?
ln(1/(e^2))=?
i would like to know the steps please:)

Answer 1

\[ln(e^x)=x\]
so \[ln(e^{-11})=-11\]

Answer 2

similarly \[e^{ln(x)}=x\]
so \[e^{ln(4)}=4\]

Answer 3

and \[e^{ln(\sqrt{3})}=\sqrt{3}\]

Answer 4

for the last one,
\[ln(\frac{1}{x})=-ln(x)\]
so
\[ln(\frac{1}{e^2})=-ln(e^2)=-2\]

Answer 5

btw \[ln(\frac{a}{b})=ln(a)-ln(b)\]so
\[ln(\frac{1}{b})=ln(1)-ln(b)=-ln(b)\]because
\[ln(1)=0\]

Answer 6

thank you !:)

Answer 7

welcome. hope it is clear!

Answer 8

oh yea def going in my notes lol :D

Answer 9

notes? ;)

Answer 10

yea so i can remember them and cram them in my head hahaha

Answer 11

well its easy just gotta remember haha