Question

solve for x

e^2x-e^x+(1/4)=0

Answer 1

like solving
\[z^2-z+\frac{1}{4}=0\]

Answer 2

then put
\[z=e^x\] and take the log to get your answer. do you need the details?

Answer 3

yes please

Answer 4

as this is a perfect square you get
\[(z-\frac{1}{2})^2=0\] so
\[z=\frac{1}{2}\] making \[e^x=\frac{1}{2}\]and thus
\[x=\ln(\frac{1}{2})\]

Answer 5

hope the steps are clear. if you want (not necessary) you can write
\[\ln(\frac{1}{2})=-\ln(2)\]

Answer 6

thanks!

Answer 7

can you help me with another question?