6*ln(4*x+2)+6=18

Solution for 6*ln(4*x+2)+6=18 equation:

Simplifying
6ln(4x + 2) + 6 = 18

Reorder the terms:
6ln(2 + 4x) + 6 = 18
(2 * 6ln + 4x * 6ln) + 6 = 18
(12ln + 24lnx) + 6 = 18

Reorder the terms:
6 + 12ln + 24lnx = 18

Solving
6 + 12ln + 24lnx = 18

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + 12ln + -6 + 24lnx = 18 + -6

Reorder the terms:
6 + -6 + 12ln + 24lnx = 18 + -6

Combine like terms: 6 + -6 = 0
0 + 12ln + 24lnx = 18 + -6
12ln + 24lnx = 18 + -6

Combine like terms: 18 + -6 = 12
12ln + 24lnx = 12

Reorder the terms:
-12 + 12ln + 24lnx = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 12ln + 24lnx = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-1 + ln + 2lnx) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(-1 + ln + 2lnx)' equal to zero and attempt to solve:

Simplifying
-1 + ln + 2lnx = 0

Solving
-1 + ln + 2lnx = 0

Move all terms containing l to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + ln + 1 + 2lnx = 0 + 1

Reorder the terms:
-1 + 1 + ln + 2lnx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + ln + 2lnx = 0 + 1
ln + 2lnx = 0 + 1

Combine like terms: 0 + 1 = 1
ln + 2lnx = 1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.