Question

What am I doing wrong? solve for x: 1+4e^(x/2)=3.

4e^(x/2)=2
e^x/2=.5
x/2=ln.5
x=2ln.5
answer: -2ln2

Answer 1

The short answer is nothing, the expressions are equivalent.

I suppose the integer one is marginally prettier.

Answer 2

1+4e^(x/2)=3
4e^(x/2)=2
e^(x/2)=1/2
lne^(x/2)=ln(1/2)
x/2=ln1-ln2
x/2=0-lnw
x=-2ln2

Answer 3

x=2ln(1/2) = 2(ln 1 -ln 2) = -2 ln 2