Solve for x (exact form): ln(x^2 *e^ -ln(sq.rtX) = 1?

Answer 1

ln(x^2 *e^ -ln(sqrt(x)) = 1
ln(x^2) + ln(e^-ln(sqrt(x)) = 1
ln x^2-ln(sqrt(x)) = 1
ln (x^2/x^1/2) = 1
x^(3/2) = e
x = e ^(2/3)

Answer 2

ln (x² e^(-ln (√x))) = 1
ln (x² * 1/√x) = 1
ln (x^(3/2)) = 1
3/2 ln x = 1
ln x = 2/3
x = e^(2/3)

And we are done.

Answer 3

lnx²e^-ln√x = 1
lnx²+-ln√xlne =1
lnx²-ln√x = 1
ln(x²/√x) = 1
e = x^3/2
x=e^2/3