How to use substitution to solve for x? ln^2 x-11lnx+30=0

We'll substitute ln x by another
variable.

ln x = t

We'll
re-write the equation in t:

t^2 - 11t + 30 =
0

We'll solve the
quadratic:

t1 = [11+sqrt(11^2 -
4*30)]/2

t1 = [11+sqrt(121 -
120)]/2

t1 = (11 + 1)/2

t1 =
12/2

t1 = 6

t2 = (11 -
1)/2

t2 = 5

Now, we'll solve
for x:

ln x = t1 => ln x = 6 => x =
e^6

ln x = t2 => ln x = 5 => x =
e^5

The values of x that represent the
solutions of the equation are: {e^5 ; e^6}.