Another calculus problem?

Question

lnx^4 - 2lnx =1

answer is square root of e

solve for x
help please!

Answer 1

lnx^4 = 4lnx
4lnx-2lnx=1
so 2lnx=1
lnx=1/2
e^ on each sides gives
x=e^1/2 , or sqrt(e)

Answer 2

Use that 2lnx = lnx^2
so that you have the following steps

lnx^4 - 2lnx =1

lnx^4 - lnx^2 =1

Then use lnA - lnB = ln (A/B)

ln(x^4 / x^2) = 1

ln( x^2 ) = 1

Exponentiate both sides

x^2 = e^1 = e

x = + sqrt( e ) or - sqrt( e )

Answer 3

lnx^4 - 2lnx =1
4lnx - 2lnx =1
2lnx=1
lnx=1/2
x = e^1/2 = sqrt e

Answer 4

By the laws of logarithms, ln x^4 = 4 ln x.
So 4 ln x - 2 ln x = 1
2 ln x = 1.
ln x = 1/2
x = e^(1/2) = √e.

Answer 5

ln (x^4/x^2)=1
(properties of logarithms)

x^2 = e^1
(put everything as a power of e and simplify)

x = sqrt e
(take the sqrt)