2ln(4x-1)+3=5

Solution for 2ln(4x-1)+3=5 equation:

Simplifying
2ln(4x + -1) + 3 = 5

Reorder the terms:
2ln(-1 + 4x) + 3 = 5
(-1 * 2ln + 4x * 2ln) + 3 = 5
(-2ln + 8lnx) + 3 = 5

Reorder the terms:
3 + -2ln + 8lnx = 5

Solving
3 + -2ln + 8lnx = 5

Solving for variable 'l'.

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

Add '-3' to each side of the equation.
3 + -2ln + -3 + 8lnx = 5 + -3

Reorder the terms:
3 + -3 + -2ln + 8lnx = 5 + -3

Combine like terms: 3 + -3 = 0
0 + -2ln + 8lnx = 5 + -3
-2ln + 8lnx = 5 + -3

Combine like terms: 5 + -3 = 2
-2ln + 8lnx = 2

Reorder the terms:
-2 + -2ln + 8lnx = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -2ln + 8lnx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1ln + 4lnx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -1ln + 4lnx)' equal to zero and attempt to solve:

Simplifying
-1 + -1ln + 4lnx = 0

Solving
-1 + -1ln + 4lnx = 0

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

Add '1' to each side of the equation.
-1 + -1ln + 1 + 4lnx = 0 + 1

Reorder the terms:
-1 + 1 + -1ln + 4lnx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1ln + 4lnx = 0 + 1
-1ln + 4lnx = 0 + 1

Combine like terms: 0 + 1 = 1
-1ln + 4lnx = 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.